Heat oil in a large heavy pot over medium high heat. Fry rosemary sprigs, turning, until crisp, about 2 minutes or just add the dried rosemary. Transfer sprigs to paper towels to drain, if using dried rosemary, after adding to the hot oil, just proceed with the next step.

Add sausage to same pot and cook, breaking up the meat and stirring occasionally, until browned and cooked through, 8-10 minutes. Transfer with a slotted spoon to a plate.

Add the chickpeas to pot and cook, tossing occasionally and mashing some chickpeas with spoon, until browned in spots, about 5 minutes. Transfer about half of chickpeas to plate with sausage. Add wine to pot, bring to a boil, and cook until liquid is almost completely evaporated, about 2 minutes.

Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until just before tender, about 3 minutes less than package directions.

Using a spider or slotted spoon, transfer pasta to pot with chickpeas and add spinach and 1 cup pasta cooking liquid. Cook, tossing often, until spinach is wilted, pasta is tender, and sauce is thickened, about 4 minutes. Add another 1/4 cup pasta cooking liquid, then gradually add 1/2 cup cheese, tossing until melted and dissolved into a luxurious, glossy sauce. Thin with more pasta cooking liquid if needed. Season with pepper, and more salt if needed. Add butter and toss to combine, then mix in reserved sausage and chickpeas.

Divide pasta among bowls. Crumble rosemary over top if using the sprigs, and sprinkle with remaining 1/4 cup cheese.