Make the sausage: Place fennel seeds and peppercorns in a spice grinder, and process until finely ground, about 30 seconds; transfer to a large bowl. Add pork, red wine, parsley, salt, paprika, and garlic; gently mix using clean hands until thoroughly combined. Set sausage aside.

Make the pasta: Bring a large pot of lightly salted water to a boil over high. Add pasta, and cook until just shy of al dente, about 2 minutes. (If using dry pasta, cook to just shy of al dente according to package directions.) Drain, reserving 2 cups of pasta cooking liquid; set aside.

Meanwhile, heat a large skillet over medium-high. Add sausage; cook, breaking into small pieces using a wooden spoon, until cooked through, 6 to 8 minutes. Add tomato sauce; cook over medium, stirring often, until sauce is deepened in color, 3 to 5 minutes. Add 1/3 cup reserved pasta cooking liquid; cook, scraping up any browned bits, until thickened, about 1 minute.

Add drained pasta to skillet, and reduce heat to medium-low. Stir in 2 tablespoons butter and 2 tablespoons reserved pasta cooking liquid; cook, stirring constantly, until emulsified, about 30 seconds. Repeat process with another 6 tablespoons reserved cooking liquid and remaining 6 tablespoons butter.

Fold Parmigiano-Reggiano into pasta mixture; cook over medium-low, stirring constantly and adding additional reserved pasta cooking liquid, 2 tablespoons at a time, as needed until a creamy sauce forms. Remove from heat; stir in parsley. Divide pasta among 4 bowls; garnish with olive oil and Parmigiano-Reggiano. Serve immediately.