1. Place the duxelles, cheese, and parsley together in a small bowl and beat until blended. Divide the mixture evenly among five of the bread slices. Spread into an even layer that extends all the way to the crusts. Top with the remaining 5 slices of bread, and press gently so the sandwiches hold together. Cut off the crusts, making neat little squares. (You can prepare the sandwiches to this point up to 1 day in advance. Wrap them tightly in plastic wrap and refrigerate until you need them.)

2. Spread both sides of each sandwich lightly with butter. Heat a griddle to medium heat and grill the sandwiches or grill them in a large heavy skillet—cast iron works well. (If you have 2 skillets, use both.) Cook until golden brown on both sides, about 6 minutes total. Remove and keep warm for up to 20 minutes on a baking sheet in a 250°F oven, if necessary, while grilling the remaining sandwiches.

3. Cut each sandwich into 4 triangles. Dip the cut edges into the chives, if using. Serve at once.