Dry the bread cubes: Spread the bread cubes on baking sheets and let them sit out uncovered overnight, or toast them at 300°F for about 20 minutes, turning once, until dry and slightly firm.

Preheat and prep dish: Preheat the oven to 375°F and butter a 9x13-inch baking dish so the stuffing doesn't stick to the edges.

Brown the sausage: Cook the sausage in a large skillet over medium heat, breaking it into small pieces with a spoon, until no pink remains and the edges turn golden, about 7 minutes. Transfer to a large bowl.

Sauté onion and celery: In the same skillet, melt the butter and add the onion and celery. Cook, stirring occasionally, until soft and translucent, about 8 minutes.

Add garlic and herbs: Stir the garlic, sage, and thyme into the skillet and cook for 1 more minute, until fragrant, then remove from the heat.

Combine bread and sausage: Add the dried bread cubes, vegetable mixture, and parsley to the bowl with the sausage. Toss gently so the bread doesn't crumble.

Season the mixture: Sprinkle the salt and pepper over the bread mixture and toss again to distribute evenly.

Whisk eggs and broth: In a separate bowl, whisk the eggs with 2 cups of the broth until blended.

Moisten the bread: Pour the egg and broth mixture over the bread a little at a time, tossing between additions, until every cube is moist but still holds its shape. Add the remaining broth if the mixture looks dry.

Transfer to baking dish: Spread the mixture evenly into the prepared baking dish, pressing down lightly with a spatula.

Bake covered: Cover the dish tightly with foil and bake for 30 minutes so the inside steams through.

Uncover and finish baking: Remove the foil and bake for another 15 minutes, until the top turns golden brown and the edges look crisp.

Rest before serving: Let the stuffing stand for 10 minutes before serving so it sets and is easier to scoop.