1. Preheat oven to 400 degrees with rack in center. Heat oil in a large skillet over medium-high. Add garlic and cook until golden, 1 to 2 minutes. Add spinach and stir until wilted. Transfer to a work surface, chop, and set aside.

2. Mix 3/4 cup bechamel with chicken. Working with one at a time, place crepe on a work surface. Arrange 1/4 cup chicken mixture and 1 heaping tablespoon spinach down center of crepe; roll into a cylinder. Transfer, seam-side down, to a 9-by-13-inch baking dish; assemble and arrange more crepes, leaving 1/2 inch in between each. Spoon more bechamel on top and sprinkle with cheese. Bake until bubbly, about 15 minutes. Switch oven to broiler setting and cook until browning in spots, about 5 minutes. Remove from oven and let cool slightly. Sprinkle with parsley.