In a bowl, whisk together 2 tablespoons olive oil, 1 tablespoon lemon juice, minced garlic, oregano, paprika, salt, and pepper. Add chicken and turn to coat evenly. Cover and marinate for at least 15 minutes at room temperature, or up to 2 hours in the refrigerator for deeper flavor.

Heat a grill pan or skillet over medium-high heat until hot. Add chicken and cook for 5 to 7 minutes per side, until golden brown with nice char marks and internal temperature reaches 165°F. Remove from heat and let rest for 5 minutes, then slice into strips or cube into bite-sized pieces.

While chicken cooks, grate cucumber using the large holes of a box grater, then squeeze firmly in a clean kitchen towel to remove excess moisture (about 2 to 3 tablespoons of liquid).

In a mixing bowl, combine Greek yogurt, squeezed cucumber, 1 tablespoon lemon juice, 1 tablespoon olive oil, minced garlic, and dill. Season with salt and pepper to taste. Stir until smooth and creamy.

In a large serving bowl, combine chopped greens, halved cherry tomatoes, sliced red onion, cucumber, Kalamata olives, and crumbled feta if using. Top with sliced chicken and drizzle generously with tzatziki dressing. Toss gently to combine.

Serve immediately for best texture contrast, or refrigerate for 10 minutes if you prefer everything chilled.