Preheat the oven to 375ºF.
Brown the sausage until browned and cooked through. Set aside.
Cook the gnocchi in boiling salted water until they float. Drain and set aside.
In a small saucepan, add the milk over low-medium heat but don’t bring it to a boil.
Meanwhile, add the butter to a medium-sized saucepan over low heat and melt. Add the flour and whisk together for about 2 minutes.
Continue whisking and add the milk, a little at a time until incorporated and no lumps remain. Cook for several minutes, whisking, until it thickens a bit.
Add the salt, black pepper, and red pepper flakes and stir.
Remove from the heat and add the cheese. Stir until the cheese is melted. Add the sausage and the gnocchi to the mixture and stir to combine.
Transfer the gnocchi mixture to a baking dish.
Bake for 30 minutes. If you would like it more browned, you can place it under the broiler (for 15-20 seconds) to brown after baking.