Adjust oven rack to middle position and heat oven to 300 degrees. Sprinkle ribs with ground fennel and season with 4 teaspoons salt and pepper, pressing spices to adhere. Heat oil in Dutch oven over medium­-high heat until just smoking. Add half of ribs, meat side down, and cook, without moving them, until meat is well browned, 6 to 8 minutes; transfer to plate. Repeat with remaining ribs; set aside.

Reduce heat to medium and add onion, fennel, carrots, 2 tablespoons sage, rosemary, and remaining ½ teaspoon salt to now-empty pot. Cook, stirring occasionally and scraping up any browned bits, until vegetables are well browned and beginning to stick to pot bottom, 12 to 15 minutes.

Add 1 cup wine and cook until evaporated, about 5 minutes Stir in tomatoes and broth and bring to simmer. Submerge garlic and ribs, meat side down, in liquid; add any accumulated juices from plate. Cover and transfer to oven. Cook until ribs are fork-tender, about 2 hours.

Remove pot from oven and transfer ribs and garlic to rimmed baking sheet. Using large spoon, skim any fat from surface of sauce. Once cool enough to handle, shred meat from bones; discard bones and gristle. Return meat to pot. Squeeze garlic from its skin into pot. Stir In remaining 2 tablespoons sage and remaining 2 tablespoons wine. Season with salt and pepper to taste.

Meanwhile, bring 4 quarts water to boil in large pot. Add pasta and 2 tablespoons salt and cook, stirring often, until al dente. Reserve ½ cup cooking water, then drain pasta and return it to pot. Add half of sauce and toss to combine, adjusting consistency with reserved cooking water as needed. Serve, passing Parmesan separately.

Note: Freeze remaining sauce for another day.