Preheat oven to 375°F.
Cook bacon in cast iron until shatteringly crispy; reserve fat and crumble bacon.
Season chicken and cook in 1–2 tbsp reserved bacon fat until golden and cooked through.
In the same pan, sauté garlic in butter 90 seconds; add cream and cream cheese and whisk until smooth and thickened.
Remove from heat; stir in parmesan in two additions until fully melted.
Combine chicken, broccoli, and most of the bacon in baking dish; pour sauce over and stir to coat.
Top with mozzarella, parmesan, and reserved crispy bacon pieces.
Bake 20–22 minutes until bubbling; broil 3–4 minutes until deeply golden.
Rest 5–8 minutes, garnish with fresh chives, and serve.