Whisk the olive oil, lemon zest and juice, garlic, oregano, smoked paprika, cumin, red pepper flakes, salt and pepper in a large bowl. Add the chicken, toss to coat and let it sit 15 minutes, or cover and refrigerate up to 8 hours.
Heat the oven to 425 degrees and line a large sheet pan. Toss the peppers and onion with the olive oil and salt.
Spread the chicken and vegetables on the pan in a single layer with a little space between pieces. Pour any extra marinade over the chicken.
Roast 22 to 25 minutes, until the chicken is browned at the edges and reads 165 degrees. For extra char, broil 2 minutes at the end.
Meanwhile, stir the yogurt, garlic, lemon juice, dill and salt together.
Rest the chicken 5 minutes, then slice. Serve with the vegetables and yogurt sauce, or cool and pack into containers.