Make the mayo: In a blender or food processor combine all ingredients and process until combined. Transfer to an airtight container and refrigerate until ready to use, can be made up to three days in advance.
Make the burgers: Gently combine the ground turkey, garlic, basil, tomato paste, mayo, red pepper flakes, and salt and pepper in a large bowl and form into 6 small 3-inch patties, pressing a small divot into the center of each patty. Refrigerate until ready to cook, can be made up to one day in advance.
Cook the burgers: Heat an oven-safe pan over medium-high heat; preheat oven broiler to high. Salt and pepper the surface of the turkey patties and drizzle pan with oil. Cook burgers about 3 to 4 minutes on each side, flipping once. Flip the burgers once more and quickly top with tomato and mozzarella cheese. Place pan under broiler and broil for 1 to 2 minutes until cheese is blistered.
Assemble burgers: Spread buns with basil mayo and top with basil, arugula, and turkey patties, drizzle with balsamic glaze or a dash of good balsamic vinegar.