Wash the lettuce. Slice the heirloom tomato into 1/2-inch thick slices and the red onion into thin half-moons. In a small bowl, combine Greek yogurt, finely diced cucumber, lemon juice, minced garlic, and fresh dill. Stir and refrigerate.

In a large bowl, gently mix the ground chicken, chopped parsley, minced garlic, salt, and pepper. Form into four 3/4-inch thick patties, making a slight thumbprint in the center of each.

Heat olive oil in a heavy-bottomed skillet over medium-high heat. Sear the patties for 5-6 minutes until a golden-brown crust forms. Flip and cook for another 5 minutes until the internal temperature reaches 165°F (74°C).

Wipe the skillet clean and lightly toast the brioche buns. On the bottom bun, layer lettuce and a tomato slice. Add the hot chicken patty, spoon on the tzatziki, scatter red onions and crumbled feta, and top with the bun.