Arrange a rack in center of oven; preheat to 425°. Spread tater tots in a single layer on an unlined baking sheet.

Bake tots until golden and very crunchy, 25-35 minutes (tots should be crunchier than you would want them to be if you were cooking them to eat immediately). Transfer to a wire rack and let cool to room temperature.

Reduce oven temperature to 375°. Grease a 13” x 9” baking dish with cooking spray.

In a large skillet over medium heat, cook sausage, stirring to break up into bite-sized pieces, until cooked through, 5 to 6 minutes. Transfer sausage to a small plate, leaving as much fat as possible in skillet.

In same skillet over medium heat, melt 4 Tbsp. butter. Add onion and celery; season with ½ tsp. salt. Cook, stirring occasionally, until softened, about 7 minutes. Add sage and thyme and cook, stirring, until fragrant, about 2 minutes more. Add remaining 4 Tbsp. butter and stir until melted, then remove from heat and let cool slightly.

In a bowl, whisk eggs and broth; season with remaining ½ tsp. salt. Add tater tots, sausage, and onion mixture (including the just-melted butter) and toss briefly to combine. (Don’t overmix, or tots will begin to fall apart!)

Pour tots mixture into prepared dish, arranging the prettiest whole tots on top if desired; cover with foil.

Bake stuffing for 20 minutes, then uncover and continue to bake until crisp on the top and an instant-read thermometer inserted into the center registers 160°, 10 to 15 minutes more. If using, top with fresh thyme before serving.