Preheat the oven to 375 degrees F and butter a shallow 3-quart baking dish. Melt 6 tablespoons butter in a large nonstick skillet over medium-high heat. Add the sausage and cook, stirring and breaking up the meat with a wooden spoon, until lightly browned and no longer pink, about 6 minutes.
Add the celery and onions and cook, stirring occasionally, until softened, about 5 minutes. Stir in the sage. Add the broth, 1 teaspoon salt and a few grinds of pepper; bring to a simmer, then remove from the heat.
Whisk the eggs in a large bowl. Add the parsley, bread cubes and sausage-broth mixture and stir until combined. Transfer the stuffing to the prepared baking dish. Cut the remaining 2 tablespoons butter into small cubes and scatter evenly over the stuffing. Cover with foil and bake 30 minutes, then uncover and bake until golden, 20 to 30 more minutes.