Put the lamb in a bowl. Using a box grater, grate the onion over the bowl so that the pulp of the onion and juices fall into the meat. Add the spices, chili pepper, egg, breadcrumbs, salt and pepper, to taste, and mix to combine. Form the meat mixture into four patties, thinner at the middle and thicker at the edges for even cooking.
Heat a large skillet over medium-high heat and coat with EVOO, or coat the burgers in EVOO and grill on an outdoor grill. Cook the patties about 10 minutes, turning once.
While the patties cook, add the yogurt to a small bowl. Grate the garlic into the yogurt using a fine grater or zester. Add the mint and stir to combine.
Char the pitas over an open gas burner or outdoor grill.
Eat the burgers in or on the pita bread topped with the garlic-mint yogurt, sliced red onion and some shredded cabbage.