Pinch 1 pound sausage into bite-sized pieces (½- to 1-inch in size) and arrange in an even layer in the bottom of a large pot or Dutch oven. Sprinkle 1 teaspoon fennel seeds and ½ teaspoon granulated garlic over top.
Place over medium heat and cook, without stirring, until deeply golden brown, 6–7 minutes. Stir and continue cooking until no longer pink, about 4–6 minutes. Using a slotted spoon, transfer sausage to a bowl and reserve drippings in pot.
Add onion wedges to drippings and cook over medium, without moving, until deeply charred, about 5 minutes (turn vent fan on!), flip onion wedges and continue cooking until second side is browned, about 3 minutes.
Meanwhile, roughly chop the stalks and fronds of one fennel bulb; sprinkle chopped stalks and fronds over onions and cook 2 minutes. Deglaze pot with 1 cup wine and cook, scraping up fond on pot, until half the liquid has evaporated, about 5 minutes.
Stir in 6 cups water, 2 tablespoons Better than Bouillon, 2 Parmesan rinds, and 2 teaspoons kosher salt; bring to a boil then reduce to a very low simmer and cook 45 minutes.
Remove from heat and let cool slightly. Strain mixture through a fine-mesh sieve lined with cheese cloth, pressing firmly on solids to release as much liquid as you can (should measure about 4 ½ cups). Discard solids then return liquid to pot; cover and bring to a boil.
Meanwhile, remove and reserve fennel fronds from remaining fennel stalks. Thinly slice the stalks then halve and thinly slice both bulbs. Stir sliced fennel stalks and bulbs into stock, cover and simmer over medium heat until fennel is tender, 6–8 minutes.
Add 4 cups tortellini and browned sausage, bring back to a simmer, cover and cook until tortellini are tender, about 3 minutes. Roughly chop reserved fennel fronds, measure ¼ cup fronds and stir into dish.
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