In large bowl, beat together eggs and milk. Add chicken to milk mixture. Cover and refrigerate for 6 to 12 hours.
Drain chicken; discard milk mixture. Roll chicken pieces in bread crumbs til coated. In a large skillet, heat 2 Tbsp. cooking oil. Add more oil as needed during cooking. Add half of the chicken; cook and stir over medium high heat for 3 to 4 minutes or til o longer pink. Remove chicken from skillet and drain on paper towels. Repeat cooking and draining the remaining chicken.
Preheat oven to 350. In greased 3 quart casserole, layer half of the chicken, half of the cheddar cheese, and half of the mozzarella cheese. Repeat layering the remaining chicken and cheese. Pour chicken broth over top. Cover land bake for 40 to 45 minutes or til heated through. makes 8 servings.