Preheat the oven to 350° and butter a large baking dish. Spread the bread cubes on a baking sheet and toast for 25 minutes, stirring, until lightly browned and crisp.
Meanwhile, in a large, deep skillet, melt the 1 stick of butter. Pour half of the butter into a small bowl and reserve. Add the celery, carrots and onion to the skillet and cook over moderately high heat, stirring occasionally, until softened and just beginning
to brown, about 8 minutes. Scrape the vegetables into a large bowl. Add the sausage to the skillet in lumps and cook over moderately high heat, breaking it up with a spoon, until lightly browned and cooked through, about 6 minutes. Return the vegetables to
the skillet, add the sage and thyme and cook for 1 minute. Add 1 cup of the stock and cook, scraping up any bits stuck to the pan, until nearly evaporated, about 5 minutes.
Scrape the sausage mixture into the large bowl and add the toasted bread cubes. Add the remaining 2 cups of stock and stir until the bread is evenly moistened. Season with salt and freshly ground pepper. Spread the stuffing in the baking dish and brush
with the reserved melted butter.
Bake the stuffing in the center of the oven for about 1 hour, until it is heated through and the top is browned and crisp. Let the stuffing stand for 10 minutes before serving.