- To make the pesto, engage the motor of a food processor and drop the garlic cloves through the feed tube. When the garlic is minced, turn off the motor and add the basil and pine nuts. Process until finely chopped.
- With the motor running, pour in the olive oil in a steady stream to make a smooth, thick paste. Transfer the pesto to a small bowl and stir in the cheese by hand. You will have about 1 cup pesto.
- Measure 6 tablespoons for stuffing the steaks; reserve the remainder for another use.
- Prepare a charcoal or gas grill for direct grilling over medium-high heat. Oil the grill rack.
- Using a small, sharp knife, make a horizontal cut into one side of each steak, forming a pocket almost to the edges of the steak; take care not to cut all the way through. Using a small spoon, stuff 1 tablespoon of the pesto into each pocket. If necessary, secure the pocket with toothpicks. Brush both sides of the steaks and tomato slices with the olive oil, and season with salt and pepper.
- Grill the steaks over the hottest part of a charcoal fire or directly over the heat elements of a gas grill, turning once, until nicely charred and cooked to your liking, 5 to 6 minutes per side for medium-rare.
- While the steaks are cooking, place the tomatoes at the edges of a charcoal grill where the heat is less intense, or on an area of a gas grill with lower heat. Grill the tomato slices, turning once with a spatula, until just softened and lightly charred, 2 to 4 minutes per side.
- Transfer the steaks to individual plates, placing each steak on or next to a tomato slice. Serve immediately.