Step 1:
Preheat the broiler and adjust the rack to 6 inches from the heat source. In a large bowl, combine yogurt, juice from half a lemon, and dried oregano. Season the mixture with salt to taste. Set aside half of the yogurt mixture in a small bowl and refrigerate for later use. Stir the garlic into the remaining yogurt marinade, then add the chicken. Toss to coat the chicken thoroughly in the marinade, ensuring even coverage.
Step 2:
On a sheet pan, toss the halved tomatoes and thinly sliced onion with olive oil and a pinch of salt. Push the vegetables to one side of the pan. Arrange the marinated chicken on the opposite side in a single layer, ensuring excess marinade is scraped off. Broil for 5 to 7 minutes, until the chicken develops a charred top, adjusting the broiler time depending on its strength.
Step 3:
Remove the sheet pan from the oven. Use tongs to flip the chicken pieces over and place the lemon slices between and under the chicken. Stir the tomatoes and onion to ensure even cooking. Return the pan to the broiler and cook for an additional 5 to 7 minutes until the chicken is fully cooked, the tomatoes are blistered, and the onions have softened and deepened in color. Meanwhile, place the pitas on a separate sheet pan on a lower rack to warm.
Step 4:
Once cooked, sprinkle the chicken with fresh mint leaves. Cut the remaining lemon half into wedges. Serve the roasted chicken and vegetables with the warm pitas, crumbled feta, mint leaves, lemon wedges, and the reserved yogurt dip on the side. Enjoy!