Heat the oven to 350 F. Lightly coat a baking dish with cooking spray.
In a pot fitted with a steamer basket, bring 1 inch of water to a boil. Add the broccoli. Cover and steam until tender-crisp, about 5 to 7 minutes.
Heat the crepes in the microwave for 30 seconds to 1 minute, or according to package directions. Place 1/4 of the turkey, 1/4 cup steamed broccoli and 2 tablespoons cheese on each crepe. Roll up and place seam-side down in the prepared baking dish. Bake until the cheese melts, about 5 minutes. Serve immediately.