Heat oil in medium skillet over medium-high heat. Add 3 tablespoons fresh sage and fry 30 seconds. Using slotted spoon, transfer fried sage to paper towel.
Combine cheese, onions, shallot, salt, and remaining 1 tablespoon fresh sage in bowl. Season with pepper. Using small sharp knife, remove cone-shaped piece 2 inches wide and 1 inch deep from top of each tomato. Divide cheese mixture among tomatoes; top with fried sage.
Prepare barbecue (medium-high heat). Place tomatoes on grill rack; cover barbecue with lid. Cook until tomatoes are soft, about 5 minutes.
