1. In a large skillet over medium heat, heat 2 tablespoons butter and the oil. Add mushrooms, and season with salt and pepper; saute until mushrooms begin to soften and juices evaporate, about 8 minutes. Add Madeira, and remove from heat; deglaze pan, stirring with a wooden spoon until liquid has evaporated. Let cool, and place in the bowl of a food processor fitted with the metal blade. Add remaining butter; pulse until mushrooms are finely chopped, about 1 minute.

2. Thinly spread two slices of bread with mushroom butter; cover one slice with a single layer each of bacon and arugula, and top with other bread slice. Use a serrated knife to trim crusts and cut in half diagonally into two triangles. Cover with damp paper towels until ready to serve. Repeat with remaining ingredients.