To prepare the crepes, lightly spoon 3/4 cup flour into dry measuring cups, and level with a knife. Combine flour and 1/8 teaspoon salt in a bowl. Add the milk, egg, and egg white, stirring with a whisk until almost smooth. Cover batter; chill 1 hour.
Place an 8-inch crepe pan or nonstick skillet coated with cooking spray over medium-high heat until hot. Remove pan from heat. Pour a scant 1/4 cup batter into pan; quickly tilt pan in all directions so batter covers pan with a thin film. Cook about 1 minute.
Carefully lift the edge of crepe with a spatula to test for doneness. The crepe is ready to turn when it can be shaken loose from the pan and the underside is lightly browned. Turn crepe over; cook 30 seconds on other side.
Place crepe on a towel; cool. Repeat procedure with remaining batter. Stack crepes between single layers of wax paper or paper towels to prevent sticking.
Preheat oven to 350°.
To prepare the filling, melt butter in a large nonstick skillet over medium heat. Add the shallots, and saute for 3 minutes. Add the mushrooms, thyme, and garlic; saute 5 minutes. Sprinkle the mushroom mixture with 3 tablespoons flour; cook 1 minute. Gradually stir in broth, sherry, 1/4 teaspoon salt, and pepper. Bring mixture to a boil; reduce heat, and simmer until thick (about 2 minutes). Remove from heat, and reserve 1/2 cup mushroom mixture. Stir the chicken into remaining mushroom mixture.
Spoon about 1/3 cup chicken mixture onto center of each crepe. Bring 2 opposite sides to center; fold over filling. Place filled crepes, seam sides down, in a 13 x 9-inch baking dish coated with cooking spray. Spoon the remaining 1/2 cup mushroom mixture over crepes, and sprinkle with cheese. Bake at 350° for 15 minutes or until thoroughly heated.