1. Bring chicken broth and milk to a gentle boil in a heavy saucepan. Slowly whisk in grits. Reduce heat to low, cover, and cook 20–25 minutes, stirring occasionally, until thick and creamy.
2. Stir in 2 tbsp butter and cheddar. Season with salt and pepper; keep warm.
3. Meanwhile, melt remaining 2 tbsp butter in a skillet over medium heat. Add garlic; cook 30 seconds. Add shrimp, season lightly, and sauté 2–3 minutes per side until pink.
4. Divide hot grits among bowls, top with garlic‑butter shrimp and pan sauce. Garnish with parsley and serve immediately.