Combine all mayonnaise ingredients into a small bowl and mix well. Cover and chill.
Combine all ingredients into a medium bowl except cheese, buns lettuce and tomato. Mix until combined.
Shape ground turkey mixture into four 1-inch thick patties.
Create a small well in the center of each pattie. Add cheese and push the turkey to cover the cheese completely. Cover the patties and chill for 1 hour.
Preheat barbecue to medium-high heat (375°F | 190°C).
Oil the grill and place burgers on grill. Grill burgers for 4 minutes, flip once and grill until a thermometer inserted in thickest part of meat registers 1165°F (75°C).
To assemble, smother mayonnaise on top and bottom buns. Place fully cooked pattie on bottom bun, then top with lettuce and tomato. Cover burger with top bun and serve.
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