1. Using your hands, gently combine turkey, cheese, roasted garlic, sage, and 1/2 teaspoon each salt and pepper in a medium bowl (do not overwork meat). Shape into 4 patties (about 5 inches in diameter). Refrigerate, covered, until cold, about 1 hour (or overnight).

2. Preheat grill to medium-high (if using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for just 3 to 4 seconds). Brush grill and burgers with vegetable oil. Grill, flipping once, until cooked through, 3 to 4 minutes per side. Toast rolls, cut sides down, on grill; brush cut sides with olive oil.

3. Whisk lemon juice and 1 tablespoon olive oil in a medium bowl; season with salt and pepper. Add watercress; toss.

4. Spread grilled-tomato sauce on bottom half of each roll. Top each with a burger, one-quarter of the watercress salad, and top half of roll.