Rinse chicken and pat dry with a paper towel. Soak chicken breasts in the eggs for at least 1 hour. Drain and roll in the breadcrumbs to coat.
Preheat oven to 350°F.
In a large skillet over medium heat, brown the chicken in melted butter and place in an 8x8 inch baking dish. Combine the mushrooms, lemon juice, wine, and broth in a medium bowl. Pour mixture over the chicken and top with slices of cheese. Cover with foil and bake 45 to 60 minutes, or until chicken is cooked thru and tender.