Mix chicken, red onion, cilantro, chili powder, yogurt, tandoori paste, lemon juice, parsley, cumin, red pepper flakes, garlic paste, ginger paste, and garam masala together in a bowl; cover with plastic wrap and marinate in refrigerator for up to 2 days.
Preheat oven to 350 degrees F (175 degrees C).
Stir bread crumbs and egg into chicken mixture; form into patties. Arrange patties on a baking sheet.
Bake in the preheated oven until cooked through, 5 to 8 minutes per side.
Heat olive oil in a skillet over medium heat; cook burgers in the hot oil until browned, 7 to 8 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).