Make the quick-pickled onions. In a small bowl, combine red onion, red wine vinegar, sugar, and a pinch of salt.
Toss and set aside while you prepare everything else. They’ll soften and turn bright pink.
Mix the tzatziki. In a bowl, combine Greek yogurt, grated cucumber (squeezed dry with a paper towel), garlic, lemon juice, dill, olive oil, salt, and pepper. Stir until creamy.
Cover and chill to let the flavors meld.
Season the lamb. In a large bowl, gently mix ground lamb with garlic, lemon zest, oregano, cumin, smoked paprika, salt, and pepper. Don’t overwork it or the patties can get tough.
Form the patties. Divide the mixture into 10–12 equal portions. Shape into 2 1/2-inch patties about 1/2 inch thick.
Press a small dimple in the center to prevent puffing.
Heat the pan or grill. Warm a cast-iron skillet over medium-high heat with 1 tablespoon olive oil, or preheat a grill to medium-high. You want a strong sizzle for a good sear.
Cook the sliders. Sear patties 2–3 minutes per side for medium, or 3–4 minutes for more doneness. Avoid pressing them down—keep the juices inside.
Transfer to a plate and rest 3–5 minutes.
Toast the buns. Brush the cut sides with a little olive oil. Toast in the skillet or on the grill until golden at the edges. Warm buns resist sogginess and add flavor.
Assemble. Spread tzatziki on the bottom bun.
Add lettuce, a lamb patty, a slice of tomato, a few pickled onions, and a sprinkle of crumbled feta. Top with more tzatziki if you like, then cap with the bun.
Serve. Garnish with extra dill or a squeeze of lemon. Serve immediately while the patties are juicy and the buns are crisp.