Preheat oven to 350 F.
Set an oven-safe skillet over medium heat on the stove.
Melt butter in skillet, add shallots and garlic and cook until softened, 1 to 2 minutes.
Add Brussels sprouts, salt, pepper, and paprika, and saute for 5 to 8 minutes.
Add chicken and stir to combine.
Remove from heat. If you do not have an oven-safe skillet, this is when you will want to transfer the Brussels sprouts and chicken to a 9 X 13" casserole dish.
Pour in heavy whipping cream.
Sprinkle both cheeses over the mixture.
Place in oven and bake about 12 minutes.
Remove from oven and sprinkle with crumbled bacon and if desired, chopped scallions