Marinate the chicken. In a bowl, whisk olive oil, lemon zest and juice, garlic, oregano, cumin, salt, and pepper.
Add chicken, toss to coat, and marinate at least 20 minutes or up to 8 hours in the fridge.
Cook the orzo. In a medium pot, warm 1 tablespoon olive oil over medium heat. Add orzo and toast 1–2 minutes, stirring. Pour in broth, bring to a boil, then simmer 8–10 minutes until al dente.
Drain any excess liquid if needed. Fluff and set aside.
Make the sauce. Stir together yogurt, grated garlic, lemon juice, olive oil, dill or mint, and a pinch of salt and pepper. Adjust lemon and salt to taste.
Chill until serving.
Cook the chicken. Heat a large skillet over medium-high. Add a light drizzle of oil. Shake off excess marinade and cook chicken 5–7 minutes per side, until browned and cooked through (165°F/74°C internal).
Rest 5 minutes, then slice.
Prep the veggies. While chicken cooks, halve tomatoes, dice cucumber, slice onion, and chop herbs. Pat olives dry for less brine in the bowl.
Season the orzo. Toss warm orzo with a splash of olive oil, a squeeze of lemon, and a pinch of salt and pepper. Fold in half the parsley and dill.
Assemble the bowls. Divide orzo among bowls.
Top with sliced chicken, tomatoes, cucumber, red onion, and olives. Add dollops of the yogurt sauce and sprinkle with feta and remaining herbs.
Finish and serve. Add lemon wedges on the side and a pinch of red pepper flakes if you like heat. Taste and adjust salt, lemon, and olive oil right in the bowl for a bright finish.