Preheat oven to 350 degrees then spray a 9x13" baking dish with nonstick spray and set aside. Brown sausage with shallot in a large skillet over medium-high heat then drain if desired and set aside to cool slightly (can be done ahead of time.) Whisk eggs, salt, and pepper in a very large bowl, add sour cream and milk, and then whisk until smooth. Add 3/4 of the shredded cheese (about 6oz,) the cooked sausage, and thawed hash browns to the bowl then stir to combine. Pour mixture into prepared baking dish then smooth with a spatula until liquid is evenly distributed. Sprinkle remaining cheese on top then cover with foil and bake for 1 hour, to 1 hour and 15 minutes, or until a knife inserted into the center comes out clean. Remove foil then bake for 5 more minutes or until top is golden brown. Let sit for 5 minutes before cutting and serving.