Melt 2 tablespoons (28g) butter in a large skillet over medium-high heat. Add sausage and mash with a stiff whisk or potato masher to break up into fine pieces (the largest pieces should be no bigger than 1/4 inch). Cook, stirring frequently, until only a few bits of pink remain, about 8 minutes. Add onion, celery, garlic, and sage and cook, stirring frequently, until vegetables are softened, about 10 minutes. Add parsley and season to taste with salt and pepper. Transfer contents to a large bowl and set aside until completely cool.
While filling cools, make knots. On a lightly floured surface, divide dough into 2 even pieces. Working with one piece at a time, roll or stretch into an oblong strip about 8 inches long and 4 inches wide. With a bench scraper or knife, cut crosswise into 12 strips. Repeat with other half of dough.
Tie each strip into a knot and transfer to bowl with sausage mixture. Toss and fold with your hands until every knot is thoroughly coated in sausage mixture. Grease a 9- by 13-inch baking dish with 1 tablespoon (14g) butter. Transfer knots to baking dish in a single layer. Drizzle with olive oil, cover tightly with plastic, and set aside until doubled in size, about 4 hours. Alternatively, refrigerate until doubled in size, 12 to 16 hours.
When ready to bake, adjust oven rack to center position and preheat oven to 425°F (220°C). Unwrap rolls. Transfer to oven and bake until golden brown and crisp, 25 to 30 minutes.
When rolls are almost ready, melt remaining tablespoon butter in the microwave or on the stovetop. Remove rolls from oven and immediately brush on butter. Serve with gravy and cranberry sauce on the side.