Preheat to 375°F. Butter a 13x9-inch baking dish.
Melt butter in a skillet over medium heat. Cook onion for 8 minutes until soft.
Add garlic; cook 1 minute. Sprinkle in flour; whisk for 1 minute.
Gradually whisk in broth and milk. Simmer 5–7 minutes until thickened.
Stir in broccoli, salt, pepper, and cayenne. Simmer uncovered 12–15 minutes.
Mix in chicken and cheddar. Stir until melted and creamy.
Pour into baking dish. Top with biscuits.
Bake 15–18 minutes until biscuits are golden and edges are bubbly.
Mix melted butter, garlic, salt, and parsley. Brush over hot biscuits.
Let rest 5 minutes before serving.