Combine the mayonnaise, fresh dill, lemon zest, lemon juice, and minced garlic together in a small bowl. Season with sea salt and freshly cracked pepper, to taste then mix well until thoroughly combined. Cover and place into the refrigerator so the flavors can mingle.
Gently combine the ground turkey with the roasted bell pepper, kalamata olives, onion, parsley, feta, garlic, oregano, basil, crushed red pepper flakes, sea salt and freshly cracked pepper, to taste, together with your fingers in a bowl until well mixed. Form into 4-5 patties.
Heat a large skillet with the olive oil and a bit of cooking spray. Once the pan is hot, place the turkey patties into the pan and cook for 6-8 minutes then flip over and continue cooking for 4-5 minutes, or until cooked through.
Toast the buns if desired. Spread some dill garlic mayonnaise on the bottom bun then place some lettuce on top followed by the turkey burger, add a little more mayo if desired followed by a thick slice of tomato and the remaining bun. Serve immediately. Enjoy!