Preheat the oven to 375 degrees F and butter a 3-quart baking dish. Melt the butter in a large pot or Dutch oven over medium heat. Add the onion, celery, sage and thyme; season with 1 teaspoon salt and a few grinds of pepper. Cook, stirring, until the vegetables are tender, about 5 minutes. Add the broth and bring to a boil, then remove from the heat.
Whisk the eggs and parsley in a large bowl. Add the bread and the vegetable-broth mixture and stir until combined. Transfer to the prepared baking dish. Drizzle with the turkey drippings (or dot with butter); sprinkle with the paprika.
Cover the dish with foil and bake 30 minutes, then uncover and bake until golden, 25 to 30 more minutes.
You can assemble this stuffing the day before - keep in the fridge until baking.