Step 1
Cook 1 medium butternut squash (1½–2 lb.), peeled, halved, seeds removed, cut into 1″ pieces (about 6 cups), in a large pot of boiling salted water until very tender, 12–14 minutes. Using a slotted spoon, transfer squash to a medium bowl. Reduce heat to low, cover pot, and leave on burner to keep warm.
Step 2
Heat 2 Tbsp. extra-virgin olive oil in a large high-sided skillet or a medium Dutch oven over medium-high. Add 1 lb. hot or sweet Italian sausage, casings removed, and break up into small pieces with a wooden spoon. Cook, undisturbed, until deeply browned underneath, about 3 minutes. Continue to cook, stirring occasionally, until browned all over and just cooked through, 3–4 minutes more. Transfer to a plate with a slotted spoon.
Step 3
Reduce heat to medium-low. Cook 3½ oz. Medjool dates (about 6), pitted, sliced lengthwise ¾” thick, in same pan, turning halfway though, until deeply browned, 3–4 minutes. Transfer to plate with sausage; season with salt.
Step 4
Add remaining 3 Tbsp. extra-virgin olive oil to pan. Add 6 garlic cloves, thinly sliced, ½ tsp. freshly ground pepper, ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt, and reserved squash. Cook, scraping up browned bits and smashing squash with spoon to break up, until lightly browned and broken up into a chunky paste (pieces do not need to be even), about 5 minutes.
Step 5
Meanwhile, return cooking liquid in reserved pot to a boil over high heat. Cook 12 oz. short tube pasta (such as rigatoni) until very al dente, about 3 minutes less than package directions (it will finish cooking in sauce). Drain, reserving 3 cups pasta cooking liquid.
Step 6
Add 1 cup pasta cooking liquid to squash and break up squash with spoon until a saucy consistency. Add pasta, another 1 cup pasta cooking liquid, and reserved sausage and dates. Increase heat to medium-high; cook, adding more pasta cooking liquid as needed, until pasta is al dente and coated in sauce, 2–3 minutes. Remove from heat and stir in 1 Tbsp. sherry vinegar or balsamic vinegar. Taste pasta and add more vinegar, salt and/or pepper if needed.
