Pre-heat the oven to 375F. Add oil to a saute pan on medium heat and saute the shallots and cook for about 2 to 3 minutes. Next add the garlic and stir for about 10 seconds.
Add the shredded brussels sprouts and season with salt and pepper. Continue to stir until tender, about 5 to 6 minutes
Then, pour in the heavy cream and top with both cheese. Mix it all together
Transfer the brussels sprouts mixture into a greased baking dish
Bake in the oven for about 12-15 minutes until the cheese is hot and bubbly