Preheat your grill to medium-high heat, around 400°F. Pat the chicken breasts dry with paper towels and brush both sides with olive oil. Season generously with salt and pepper. While the grill heats, make the sauce.

In a small mixing bowl, combine Greek yogurt, minced garlic, lemon juice, and dried parsley. Whisk until smooth and creamy. Taste and adjust seasoning with a pinch of salt if needed. Set aside.

Place the chicken on the preheated grill and close the lid. Cook for 6-7 minutes without moving it. Flip once and cook for another 6-7 minutes until the internal temperature reaches 165°F.

While the chicken grills, fill a pot with about 2 inches of water and bring to a boil. Place broccoli florets in a steamer basket over the boiling water, cover, and steam for 4-5 minutes until tender-crisp and bright green.

Remove chicken from the grill and let it rest for 5 minutes before slicing against the grain into strips.

Divide steamed broccoli between serving bowls, top with sliced grilled chicken, and drizzle generously with the creamy garlic sauce. Serve immediately.