Preheat the oven to 375 degrees F and butter a 3-quart baking dish. Melt 6 tablespoons butter in a large pot or Dutch oven over medium-high heat. Add the sausage and cook, breaking up the meat with a wooden spoon, until lightly browned and cooked through, about 7 minutes.
Add the celery, onions, thyme, rosemary, 1 teaspoon salt and a few grinds of pepper to the pot. Cook, stirring occasionally, until the vegetables are tender, about 5 minutes. Add the kale and cook, stirring, until just softened, about 3 minutes. Add the chicken broth and bring to a simmer, then remove from the heat and set aside.
Whisk the eggs and parsley in a large bowl. Add the bread cubes and the sausage mixture; stir to combine. Fold in the provolone. Transfer the stuffing to the prepared baking dish. Cut the remaining 2 tablespoons butter into cubes and dot over the stuffing. Cover with foil and bake 30 minutes, then uncover and bake until golden brown, about 20 more minutes.