Working in batches if necessary, pulse the fresh mushrooms and dried porcini mushrooms in a food processor until very finely chopped.
1 ½ pound mixed mushrooms, ⅛ ounce dried porcini mushrooms
In a large sauté pan, heat the olive oil and butter over medium heat.
1 tablespoon extra virgin olive oil, 4 tablespoon unsalted butter
Add the mushroom mixture to the pan, cover it with a lid, and sweat the moisture out of the mushrooms.
While mushrooms sweat, pulse the chestnuts, shallots, garlic, and thyme until finely chopped.
½ cup chestnuts, 2 shallot, 3 clove garlic, 4 –5 sprig fresh thyme
Remove the lid from the mushrooms, and continue to cook until the mixture is mostly dry. Add the chopped aromatics and Madeira wine, and stir to combine. Season with salt and pepper to taste.
¼ cup Madeira wine, Kosher salt & freshly ground black pepper
Cook, stirring often, until the mixture is fragrant, dry, and darkened in color.
Let cool completely.