Gently brush any dirt from the mushrooms using a pastry brush or paper towel. Slice the mushrooms into 1/4-inch thick pieces.
In a medium bowl, mix together the sherry and olive oil, a couple tablespoons of each. Add the mushrooms, the thyme and season with salt and pepper. Toss the mixture gently to ensure the mushrooms are well coated. Allow to marinate about 10 minutes, stirring occasionally.
Meanwhile, brush both sides of the bread slices with olive oil. You can put these in the oven to broil but I recommend using a stovetop grill or large sauce pan. Grill both sides just slightly over medium-high heat, just about 1 min per side. This makes the bread crispy on the outside and chewy on the inside…perfect for your crostini. Remove from the grill, lightly rub one side of each slice with the garlic clove and season with a bit of salt. Optional: Spread a bit of goat cheese over each crostini.
Set a medium skillet to warm over medium to medium-high. Remove the mushrooms from the marinade, reserving the marinade, and add to the skillet. Cook, stirring occasionally, for about 7 minutes or until the mushrooms have released their liquid and reabsorbed it. Remove the mushrooms to a plate.
Add about 3 tablespoons of the reserved marinade to the skillet and increase heat to medium-high. Allow the mixture to reduce for about 2 minutes. Add in the chilled butter and allow it to melt. Remove the pan from the heat and add the mushrooms, stirring to coat.
Spoon the mushroom mixture onto the crostini. Drizzle any remaining marinade from the skillet over the crostini, top with Parmigiano-Reggiano and serve immediately.