Step 1: Marinate the chicken in a bowl with 2 tablespoons of olive oil, lemon juice, salt, and pepper for at least 15 minutes.
Step 2: Preheat your grill or grill pan to medium-high heat. Toss the broccoli florets with the remaining 1 tablespoon of olive oil.
Step 3: Place the chicken on the grill and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F.
Step 4: Add the broccoli to the grill during the last 8-10 minutes of chicken cooking time, turning occasionally until charred and tender.
Step 5: While grilling, prepare the sauce by melting butter in a small pan. Sauté the minced garlic for 1 minute until fragrant.
Step 6: Whisk in the heavy cream and let it simmer for 3-4 minutes until slightly thickened. Stir in the Parmesan cheese and parsley.
Step 7: Slice the grilled chicken and divide it among four bowls with the grilled broccoli.
Step 8: Generously drizzle the creamy garlic sauce over each bowl and serve immediately.