Paula grills fresh tomatoes with garlic and olive oil. Garlic grilled tomatoes are very versatile. You can serve them up as an appetizer, side dish, or even as an entire meal. Follow Paula Deen as she shows you the best way to grill garlic tomatoes. his cooking how-to video is part of Paula's Home Cooking show hosted by Jamie Deen, Paula Deen. Paula Deen, owner of Lady and Sons, a famous Savannah restaurant, is Food Network's resident southern chef. Step inside her kitchen and discover delicious food that's both uncomplicated and comforting.