Bring a large pot of water to a boil and add cauliflower. Cook for 3 minutes and add broccoli to the pot and cook for 2 more minutes. Drain well and set aside.
Chop bacon and cook in a pan until crisp. Remove bacon but save 1 Tablespoon bacon fat.
Add garlic to the bacon fat and cook until fragrant, about 30 seconds. Add cream cheese and dill, cook until melted and creamy.
Stir in cream and broth and simmer for 3 minutes. Remove from heat and stir in ½ cup of cheddar cheese.
Toss sauce with vegetables and chicken. Place in a baking dish, top with remaining cheese, and bake for 20 minutes or until bubbly.