Adjust rack to top position and preheat oven to 450 degrees. Wash and dry produce.

Cut potatoes into ½-inch-thick wedges. Halve, peel, and thinly slice onion. Trim ends from cucumber. Using a peeler, shave cucumber lengthwise into ribbons, rotating as you go, until you get to the seedy core; discard core.

Toss potatoes on a baking sheet with a drizzle of oil, half the garlic powder, half the oregano, salt, and pepper. (You’ll use the rest of the garlic powder and oregano later.) 

Roast on top rack until browned and tender, 20-25 minutes.

While potatoes roast, in a small microwave-safe bowl, combine onion, vinegar, ½ tsp sugar (1 tsp for 4 servings), salt, and pepper. Cover with plastic wrap and microwave for 1 minute.

Carefully remove plastic wrap and set aside to pickle, stirring occasionally, until ready to serve.

In a separate small bowl, combine sour cream and tzatziki.

Set aside until ready to serve.

In a medium bowl, combine lamb*, half the feta, remaining garlic powder, and remaining oregano.

Form lamb mixture into two patties (four patties for 4 servings), each slightly wider than a burger bun. Season all over with salt and pepper.

Heat a drizzle of oil in a large pan over medium-high heat. Add patties; cook to desired doneness, 3-5 minutes per side.

While patties cook, halve buns; toast until golden brown.

Spread buns with as much tzatziki as you like. Fill with patties, shaved cucumber, and as many pickled onions (draining first) as you like.

Divide burgers and potato wedges between plates. Top potatoes with remaining tzatziki, remaining pickled onion, and remaining feta. Serve.