Slice bread into 1 1/2-in.-thick slices and tear into irregular 1- to 2-in. pieces. Spread on a rimmed baking sheet and leave to dry at room temperature until needed (up to 2 days). For the best stuffing, the bread should be very dry.
Preheat oven to 350°. Cook Italian sausage in a large frying pan over medium heat until lightly browned. Transfer to a large bowl with a slotted spoon. Add enough melted butter to fat in pan to yield about 2 tbsp. total fat.
Add onion, celery, herbs, and 1/2 tsp. each salt and pepper to hot pan. Cook until onions are translucent and celery is tender-crisp, about 15 minutes. Stir in spinach and cook until just wilted (add in batches if necessary). Transfer to a large bowl.
Add torn bread and broth to vegetables and mix in until bread is soaked. Add salt and pepper to taste. Stir gently to combine.
Generously coat a 9- by 13-in. glass baking pan with 1 tsp. reserved melted butter. Pour stuffing into pan and drizzle with remaining melted butter.
Cover with foil; bake 25 minutes. Remove foil and bake until starting to brown on top, about 30 minutes more.
Make ahead: Up to 2 days, chilled. Reheat at 350°, covered, until hot (about 30 minutes). Remove foil and cook 10 more minutes for a crunchy top layer.