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Slice the ciabatta into 1/2-inch thick slices. Using a 1-inch circle cutter, cut the slices into circles.
Slice the cheese into 1/8-inch thick slices. Use the circle cutter to make circles of cheese; you’ll need 1 circle of cheese per 2 circles of bread.
Zest half a truffle into a small bowl. Stir in the mustard. Spread mustard onto each circle of ciabatta.
Add a circle of cheese and sandwich ciabatta together mustard sides in.
Zest the remaining truffle into another bowl. Stir in Parmesan cheese and parsley.
Heat 2 tablespoons butter in a large skillet. Add 8 sandwiches. Cook covered for 2 minutes. Flip. Cook until golden. Remove to a sheet pan.
Season with salt and cover. Add more butter to the pan and continue cooking all of the sandwiches.
Sprinkle Parmesan cheese over the sandwiches and drizzle very lightly with truffle oil. Serve warm.