Trim chicken of any fat and pat dry. Combine almonds and bread crumbs in a shallow dish. Place flour and beaten eggs in separate shallow bowls.
Lightly dust each breast with flour and shake off excess; dip in beaten egg, shaking off excess, then coat with almond mixture.
Heat oil and 1 tablespoon of the butter in a large ovenproof skillet over medium heat. Place chicken, smooth side down, in skillet and cook until lightly browned, about 4 minutes. Turn breasts over, cook 1 more minute, then place skillet in a 375°F oven. Bake until chicken is golden brown and no longer pink inside, about 8 to 10 minutes.
Remove chicken from pan and place on warm plates. Melt the remaining 3 tablespoons butter in the hot skillet and stir in TABASCO® Buffalo Style Sauce; brush or drizzle over chicken and serve at once.
Makes 4 servings.