Turkey Cheddar Burgers

Ingredients

• 0.3 teaspoon pepper black
• 5 ounces sharp cheddar cheese extra-sharp cut into 4 (1/2-inch-thick) slices
• 2 teaspoons apple cider vinegar 
• 1.5 pounds pd of ground turkey (not labeled "all breast meat")
• 4 servings romaine leaves 
• 0.3 cup mayonnaise 
• 0.3 cup sun-dried olives drained
• 2 tablespoons olive oil 
• 0.3 teaspoon salt 
• 0.3 cup shallots finely chopped
• 4  portugese rolls 
• 1 tablespoon water 

Equipment

• food processor
• bowl
• frying pan
• baking sheet
• oven
• blender
• grill
• wax paper
• grill pan

Directions

1. Put oven rack in middle position and preheat oven to 350°F.
2. Cook shallot in oil with salt and pepper in an 8-inch skillet over moderate heat, stirring occasionally, until golden, 2 to 3 minutes, then transfer to a bowl.
3. Add turkey and mix gently but thoroughly.
4. Turn out turkey mixture onto a sheet of wax paper and divide into 8 equal mounds. Pat 1 mound into a 4-inch patty and top with 1 piece of cheese, then put a second mound on top, patting it onto other patty to enclose cheese. Pinch edges together to seal and shape into a single patty. Make 3 more burgers in same manner.
5. Heat an oiled well-seasoned ridged grill pan over moderately high heat until hot but not smoking, then grill burgers, turning over once, until just cooked through (no longer pink), 8 to 9 minutes total.
6. While burgers are cooking, heat rolls on a baking sheet in oven until crusty, about 5 minutes.
7. Transfer rolls to a rack to cool slightly.
8. Purée tomatoes with water, vinegar, and salt in a blender or mini food processor, scraping down sides as necessary, then blend in mayonnaise.
9. Cut rolls in half horizontally (if necessary) and spread cut sides with tomato mayonnaise.
10. Serve burgers on rolls with lettuce.