In a small bowl, stir together Greek yogurt, lemon juice, dill, grated garlic, and a pinch of salt. Cover and refrigerate until needed.

In a large bowl, combine ground chicken, panko, beaten egg, minced garlic, onion powder, salt, pepper, and parsley. Gently mix with your hands just until combined—do not overwork.

Divide mixture into 4 equal portions. Shape each into a patty about 3/4-inch thick, making a slight indentation in the center with your thumb. Place on a plate, cover with plastic wrap, and refrigerate for 10 minutes.

Heat a grill or grill pan over medium-high heat. Lightly oil the grates or pan. Cook patties for 4-5 minutes per side, until golden brown and an instant-read thermometer reads 165°F in the center.

During the last minute of cooking, place brioche buns cut-side down on the grill or in a separate dry skillet to toast until lightly golden.

Spread a generous tablespoon of herbed yogurt sauce on both bun halves. Place lettuce on the bottom bun, then the chicken patty, tomato slice, and red onion. Close with the top bun and serve immediately.