Preheat oven to broil.
In a 10-inch cast-iron skillet, cook bacon over medium heat until crisp. Remove bacon using a slotted spoon, and let drain on paper towels, reserving 1 tablespoon drippings in skillet.
Add broccoli to skillet; cook until bright green and heated through, 2 to 3 minutes. Remove from skillet.
Add butter to skillet, and melt over medium heat. Add garlic and flour, whisking to combine. Gradually whisk in milk until thickened. Stir in 1 cup cheese until melted.
Stir in cooked pasta, cooked chicken, salt, pepper, bacon, and broccoli. Top with remaining 1 cup cheese.
Broil 5 inches from heat until cheese begins to brown, about 2 minutes.
