Preheat oven to 450°. On a baking sheet, toss gnocchi with 2 tablespoons oil; season with salt. Spread in an even layer.
Bake gnocchi until golden brown, 20 to 30 minutes.
Meanwhile, in a large skillet over medium heat, heat 1 tablespoon oil. Add sausage and cook, breaking up meat with a wooden spoon, until no longer pink, about 8 minutes. Using a slotted spoon, transfer to a large bowl.
In same skillet over medium heat, cook onion and celery, stirring, until softened, about 8 minutes. Add garlic, sage, and thyme and cook, stirring, until fragrant, about 1 minute more. Add spinach and cook, stirring occasionally, until wilted, about 2 minutes; season with salt and pepper. Transfer to bowl with sausage.
Add gnocchi to bowl with sausage and stir to combine.
In a small bowl, whisk eggs and broth. Pour over gnocchi and stir to coat.
Reduce oven temperature to 350°. Grease a 13" x 9" baking pan with oil. Pour in gnocchi mixture, stirring to distribute.
Bake stuffing until center is set, 40 to 50 minutes. Let cool 10 minutes before serving.
