1 pound 90% lean ground sirloin 1 tablespoon ground Aleppo pepper 2 teaspoons ground cumin 1 1/8 teaspoons kosher salt, divided 1/2 teaspoon black pepper, divided 2 tablespoons plus 2 tsp. extra-virgin olive oil, divided 1 English cucumber, halved lengthwise and thinly sliced (about 2 1/2 cups) 1 cup thinly sliced red onion 1/2 cup chopped fresh mint, divided 2 tablespoons plus 1 tsp. red wine vinegar, divided 1/3 cup plain whole-milk Greek yogurt