In a large bowl, combine the ground turkey, egg, bread crumbs, onion, garlic, salt, pepper, basil, thyme, red pepper flakes, parsley, mint, and oregano until evenly mixed. Divide into 8 even portions and shape into oblong patties, placing them on a baking sheet, lined with parchment paper. Drizzle with olive oil.

Heat an outdoor grill or stove-top grill pan to medium-high. Once hot, grill the patties for about 10 to 12 minutes, flipping them over halfway through cooking. The patties should have an internal temperature of 165 degrees (check with an instant read thermometer). Remove from the grill onto a plate or platter and let rest for about 10 minutes.

Meanwhile, to make the tzatziki sauce, stir the yogurt, cucumbers, lime juice, garlic, parsley, dill, salt and pepper until evenly combined. Taste and adjust seasoning accordingly, adding more salt and pepper as needed. This can be made a day or two in advance and stored in the fridge until ready to use.

To assemble the burgers, warm the pita bread in a hot oven or on a dry skillet. Cut in half and carefully split open. Fill each half with lettuce, tomato, grilled turkey patty, sliced red onion, feta, and sauce. Serve immediately and enjoy!