Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add sliced onion and mushrooms to pan; sauté 5 minutes or until mushrooms release their moisture and darken. Stir in chicken, green onions, 1/4 teaspoon salt, and spinach.
Melt butter in a small saucepan over medium heat. Add flour to pan; stir with a whisk until blended. Cook 1 minute, stirring constantly. Gradually add milk to pan, stirring constantly with a whisk; cook 5 minutes or until thick. Remove from heat. Stir in remaining 1/2 teaspoon salt and pepper. Pour milk mixture over chicken mixture; stir to combine.
Spoon about 1/2 cup chicken mixture in the center of each crepe; fold ends and sides over. Place, seam side down, in a 13 x 9-inch baking pan coated with cooking spray. Sprinkle crepes evenly with cheese. Broil 2 minutes or until lightly browned.