Preheat oven to 375°F. Lightly oil a 9x13-inch baking dish.
Toss tater tots on the bottom of the dish in a single layer.
Heat oil in a skillet over medium. Cook andouille 5 minutes until browned. Remove and set aside.
In same skillet, cook onion and peppers 5 minutes until soft. Stir in smoked paprika and Cajun seasoning. Cool slightly.
Whisk eggs, milk, salt, and pepper in a bowl. Stir in cooked andouille, onions, and 1 cup cheese.
Pour egg mixture over tater tots. Sprinkle remaining 1/2 cup cheese on top.
Bake 35–40 minutes until set and golden. Let rest 5 minutes before slicing.