Marinate chicken breasts in olive oil, minced garlic, salt, pepper, and lemon juice for 30 minutes.
Preheat your grill to medium-high heat; cook chicken for 6-7 minutes per side until juices run clear.
Steam broccoli florets for 4-5 minutes until bright green and tender-crisp.
In a saucepan, combine sour cream, chicken broth, remaining minced garlic, Italian herbs, salt, and pepper; warm gently without boiling.
Slice grilled chicken and assemble bowls with steamed broccoli topped with chicken and a generous drizzle of creamy garlic sauce.
Garnish with freshly grated Parmesan cheese and an extra squeeze of lemon if desired.