Cook 1 lb. multicolor Peewee potatoes or other very small potatoes in a medium pot of boiling salted water until fork-tender, 10–12 minutes. Drain and set aside.
Pat dry 1 lb. large shrimp, peeled, deveined, with paper towels; season with kosher salt and freshly ground pepper. Heat 3 Tbsp. extra-virgin olive oil in a large skillet over medium-high. Arrange shrimp in an even layer and cook, undisturbed, until golden brown underneath, about 2 minutes. Toss and continue cooking, tossing occasionally, until opaque, about 1 minute more. Using a slotted spoon, transfer shrimp to a plate.
Heat remaining 1 Tbsp. extra-virgin olive oil in same pan. Add reserved potatoes and season with kosher salt and pepper. Cook, tossing occasionally, until lightly browned in spots, about 4 minutes. Add 3 garlic cloves, thinly sliced, 3 Tbsp. drained capers, and 1 Tbsp. finely chopped oregano and cook, stirring occasionally, until garlic is softened and mixture is fragrant, about 2 minutes. Add 3 Tbsp. unsalted butter and cook, tossing occasionally, until almost completely melted, then return shrimp to pan. Add juice of 1 small lemon, season with kosher salt, and toss to combine.
Transfer shrimp and potatoes to a platter or large shallow bowl and top with oregano sprigs, zest of 1 small lemon, flaky sea salt, and more pepper.