Heat oven to 300°F (149°C). Spread bread cubes on a rimmed baking sheet and dry for 20–25 minutes, stirring once, until firm and dry but not deeply browned. Transfer to a large mixing bowl. Increase oven to 350°F (177°C). Grease a 9-by-13-inch baking dish with 1 teaspoon of the measured butter.

While the bread dries, cook the sausage in a large skillet over medium heat, breaking it into crumbles, until browned and cooked to 160°F (71°C), about 8–10 minutes. Drain off rendered fat and transfer sausage to a plate.

Melt the remaining butter in the skillet. Cook onion and celery for 8–10 minutes, until soft. Stir in ground sage and pepper. Remove from heat, add sausage, and cool until warm rather than hot.

Whisk the eggs and cool broth together. Add the sausage-vegetable mixture and parsley to the bread, plus optional chopped fresh sage. Pour the egg-broth mixture over gradually, folding gently. Let stand 5 minutes so the bread absorbs liquid; it should be moist without a large puddle. Do not taste the uncooked egg mixture.

Transfer loosely to the baking dish. Cover with foil and bake 25 minutes. Uncover and bake 20–25 minutes more, until golden and the center reaches 165°F (74°C). Rest 10 minutes before serving eight portions. Refrigerate leftovers within two hours, use within 3–4 days, and reheat to 165°F (74°C).