Sprinkle cutlets evenly with allspice, salt and pepper. Heat the oil in a large, deep skillet with a tight-fitting lid over medium-high heat.
Add cutlets and brown for 2 minutes per side. Add broth and whisk up all of the browned bits from the bottom of the pan. Stir in brown sugar, vinegar, garlic, onion and apples.
Reduce skillet heat, cover and cook for 15 to 20 minutes or until cutlets are cooked through. Serve immediately.