Combine molasses, vinegar, mustard and Worcestershire sauce. Pour into a resealable plastic bag; add onion, garlic and turkey breast. Shake to coat turkey and refrigerate for 8 hours.
Set a gas grill to medium-high for indirect grilling or the coals in a charcoal grill to medium-hot for indirect grilling. Lightly coat grill rack with oil or nonstick cooking spray.
Remove turkey from plastic bag and pour marinade into a small saucepan. Season turkey with 1/4 teaspoon of the salt and 1/8 teaspoon of the pepper. Grill on indirect heat, covered, for 40 minutes, turning once or until internal temperature reaches 160 degrees. Brush with marinade a few times during cooking. Add corn to grill during last 10 minutes of cooking time, brushing with marinade and turning so all sides are lightly charred.
Add broth to remaining marinade in saucepan and simmer for 3 minutes. Season turkey and corn with remaining 1/4 teaspoon salt and 1/8 teaspoon pepper. Serve with broth mixture.