Here is a recipe for Mushroom Ketchup using American measurements.
I haven't tried it myself but all these posts have inspired me to give
it a try. The recipe does not give an amount for the vinegar -- I think
that must be a typo -- so I guess the best approach is to add vinegar
little by little until the desired piquancy is achieved.

BTW, someone in another thread was talking about early catsups
in terms of condiments. My impression from reading old cookbooks
is that they were used to flavor sauces and gravies. I didn't think
they made it to the table for individual diners to use as condiments.
Anyone think otherwise?

Mushroom Ketchup

3/4 ounce (1 package) dried boletus (porcini or cepes) (optional)
3 pounds mushrooms
2 tablespoons sea or pickling salt
1 whole pod cayenne pepper, or 1/4 teaspoon crushed hot red pepper flakes
1/2 teaspoon whole black peppercorns
1/2 teaspoon whole allspice
1/2 teaspoon whole cloves
1 or 2 blades mace, broken up, or large pinch of powdered mace
1/2 nutmeg, crushed
2 bay leaves
1 teaspoon grated fresh ginger root
2 large shallots
4 to 6 garlic cloves
Red wine vinegar
2 tablespoons red wine

I. If you are using the dried mushrooms, spread them in a heatproof
bowl. Bring 1 cup of water to a full boil, and pour it over them. Let
them steep for half an hour, then lift the mushrooms out carefully,
dipping them in the water to loosen any sand that may be attached. Put
them in a saucepan that will hold all their soaking water comfortably.
Pour the water over the mushrooms, through a coffee filter or an undyed
paper towel, and turn on the heat to medium. Cook the mushrooms until
the liquid has evaporated and been absorbed, stirring frequently to keep
them from sticking or scorching. Turn off the heat and let them cool.

2. Wipe the fresh mushrooms with a dry towel to remove any grit that may
be clinging to them. If they are very large, break them into several
pieces. Put a layer of them in the bottom of a ceramic or stone crock
with the reconstituted wild mushrooms, if using, and their juice.
Sprinkle them liberally with salt. Put on another layer of mushrooms and
salt, continuing until all the mushrooms and salt are used.

3. Cover the crock tightly and set it in a cool, dark place. (If your
house is particularly warm [more than 70° F.], this had better be the
refrigerator, because the mushrooms will mold on the top if allowed to
sit for too long at too high a temperature.) After the mushrooms have
steeped for only a few minutes, they will begin to wilt. Within an hour
or two, the contents of the crock will have reduced by half. Let them
steep for at least 24 hours, pressing on them from time to time with a
clean spoon.

4. After the mushrooms have steeped for the allotted time, set a food
mill or large wire sieve over a stainless-steel or enameled kettle large
enough to hold the contents of the crock. Force the mushrooms through
the mill or sieve, along with all their juices that have accumulated,
into the saucepan. (Don't use a food processor; it will puree the
mushrooms too fine.)

5. Add the cayenne or pepper flakes, peppercorns, allspice, cloves,
mace, nutmeg, bay leaves, and ginger. Crush the shallots and garlic and
add them to the kettle. Turn on the heat to medium. Bring the mixture to
a boil, reduce the heat to a simmer, and cook uncovered for about 45
minutes, until the ketchup is fragrant and somewhat reduced. Turn off
the heat and let it cool completely.

6. Strain the mixture through a fine wire sieve into a measuring cup,
pressing hard to get all the liquid extracted. Discard the solids. Wipe
out the kettle, then measure the juice and return it to the kettle. If
there is more than 1 3/4 cups, bring it back to a brisk boil and reduce
it to that amount. Add the vinegar and wine, then reduce the heat to
medium. Let the ketchup simmer gently for about 5 minutes more. Turn off
the heat and pour it, while still hot, into a sterilized heatproof jar
or bottle.

7. Seal the jar or bottle and let it cool, then refrigerate it.
Stored in the refrigerator, it will keep for several months.

Makes 16 ounces (1 pint)

NOTES: This recipe sounds time-consuming, but actually it is not. I
estimate that, all totaled, only about three-quarters of an hour of my
time is required. The rest of the time (steeping, simmering, etc.) is
pretty much unattended.

On the ingredients: Too much salt will make the mixture coarse and
banal, not enough will invite spoilage, so be judicious. Many English
recipes specify white wine rather than red, which makes a distinct
difference in flavor. If you elect to substitute it, also use white wine
vinegar. As to the mushrooms: remember that early cooks used only wild
mushrooms. If you can get wild mushrooms, please feel free to use. The
little white button mushrooms from the supermarket are lost in this
strongly flavored sauce unless you combine them, as Bill Neal suggested,
with dried Boletus edulis as outlined here. All the old recipes used
allspice and ginger; most Southern recipes included cayenne and either
nutmeg or mace and, occasionally, both. Less frequently used were black
pepper, cloves, shallots, and garlic, though they were usual in
eighteenth-century English recipes. --- This recipe comes from Classical
Southern Cooking by Damon Lee Fowler.