Preheat barbecue or indoor grill to medium, medium-high heat. Combine the first nine ingredients in a bowl. Moisten your hands with cold water and shape the meat into 4, 3/4" thick patties. Lightly oil the bars of your grill. Grill the patties 4 minutes per side, or until entirely cooked through. Divide and top with the cheese and cook one minute more, until the cheese is melted. Spread the buns with mayonnaise. Top bottom buns with salad greens and set on the turkey patties. Top with salsa and top buns and serve.