Put the fresh mushrooms in a food processor and pulse until roughly chopped. Transfer to a large bowl; sprinkle with the salt and mix until the salt is distributed evenly. Cover with a cloth and let sit at room temperature for about 24 hours, stirring 3 or 4 times (the mushrooms will turn dark).
An hour before you�re ready to make the sauce, put the dried mushrooms in a medium bowl and cover with about 2 cups boiling water. Use a plate if necessary to keep them submerged and soak until soft, about an hour.
Transfer the fresh mushrooms to a food processor. Use a slotted spoon to move the dried mushrooms to the processor. Then ladle or pour in � cup of their soaking liquid, trying not to disturb the grit settled at the bottom of the bowl. Add the vinegar, shallot, garlic, and lots of pepper; pur�e until smooth.
Put the mushroom mixture in a pot over medium-high heat and bring to a boil, stirring occasionally. Lower the heat so it bubbles gently and cook, stirring occasionally, until the mixture appears homogenous and thick, an hour or so. (To test the consistency, dab a small spoonful onto a plate and let sit for a few minutes; if liquid is released, it needs to cook longer.)
Cool until safe to handle, then put the ketchup in a blender and pur�e until smooth, almost velvety in texture. Add the Marsala if you�re using it and adjust the seasoning.
If using, stir in granulated sugar in � cup increments, to taste.
Let cool to room temperature, then serve or store, refrigerated, in a covered container for up to 2 weeks.
Makes about 1 quart
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