In a covered 10- to 12-inch nonstick frying pan over high heat, frequently stir mushrooms and butter until mushrooms are juicy, about 5 minutes.
Uncover and stir often until liquid evaporates and mushrooms are lightly browned, about 5 minutes more.
Stir chopped arugula with mushrooms just until wilted, about 2 minutes. Remove from heat.
Stir Boursin cheese to soften. Spoon 1/8 of the cheese onto a quarter section of each crepe. Smash cheese down slightly (crepes tear easily). Mound 1/8 of the mushroom mixture over cheese on each crepe and sprinkle mushrooms equally with parmesan.
Fold creêpes in half over filling, then in half again to make a triangle. Set triangles, 3-layer side down, slightly apart in 2 nonstick or lightly oiled 10- by 15-inch pans.
Bake in a 400° oven until filling is hot in the center and crêpe edges are crisp, about 6 minutes; switch pan positions after 3 minutes. Transfer crêpes to plates.