Mix the cucumber, yogurt, cilantro, 1/2 teaspoon salt, and pepper to taste in a bowl. Set aside while you make the burgers.
Combine the beef, onion, garlic, curry powder, 1/2 teaspoon salt and 1/8 teaspoon pepper in a bowl and mix with your hands until just combined. Form into four 4-inch-wide patties, about 1/2 inch thick.
Heat the olive oil in a large cast-iron skillet over medium-high heat. Add the burger patties and cook, turning once, until cooked through, 7 to 8 minutes for medium.
Place the burgers on the buns. Stir the cucumber-yogurt mixture and spoon on top. Serve the burgers with sweet potato chips and pickled okra.