Marinate the chicken. In a bowl, whisk olive oil, lemon juice and zest, garlic, oregano, cumin (if using), salt, and pepper.
Add chicken and toss to coat. Let it sit for at least 20–30 minutes, or up to 8 hours in the fridge.
Prep the vegetables. While the chicken marinates, chop the greens, slice the cucumber and onion, halve the tomatoes, and dice the pepper. Set aside the olives, feta, and parsley.
Make the dressing. Whisk olive oil, red wine vinegar, lemon juice, Dijon, oregano, garlic, and honey.
Season with salt and pepper. Taste and adjust acidity or sweetness as needed.
Cook the chicken. Grill over medium-high heat for 5–7 minutes per side, or pan-sear in a lightly oiled skillet for the same time. Cook until the thickest part reaches 165°F (74°C).
Rest for 5 minutes, then slice.
Assemble the salad. In a large bowl or platter, layer greens, cucumber, tomatoes, onion, and bell pepper. Add sliced chicken, olives, and feta. Sprinkle with parsley.
Dress and serve. Drizzle with dressing just before serving and toss gently.
Finish with a squeeze of lemon and a crack of black pepper for brightness.