01 - In a large bowl, whisk together olive oil, lemon juice, minced garlic, smoked paprika, ground cumin, dried oregano, crushed red pepper flakes, salt, and black pepper until well combined.
02 - Add chicken breasts to the marinade, turning to coat evenly. Let marinate for at least 15 minutes at room temperature, or refrigerate for up to 2 hours for deeper flavor penetration.
03 - Preheat grill or grill pan over medium-high heat until hot. Lightly oil the grates to prevent sticking.
04 - Place marinated chicken on the preheated grill. Cook for 6 to 7 minutes per side, or until internal temperature reaches 165°F and juices run clear. Transfer to a cutting board and let rest for 5 minutes.
05 - While chicken rests, combine diced cucumber, halved cherry tomatoes, sliced red onion, Kalamata olives, and chopped fresh parsley in a large mixing bowl.
06 - Drizzle extra-virgin olive oil and red wine vinegar over the vegetables. Toss gently to combine without crushing the tomatoes. Season with salt and black pepper to taste.
07 - Slice the rested chicken against the grain into strips. Arrange over or alongside the cucumber salad. Garnish with fresh lemon wedges and additional parsley if desired.