Bring a large pot of water to a boil.
Heat 3 tablespoons butter in a large 12-inch stainless steel skillet over medium heat until melted. Add 1 diced onion and 4 cloves minced garlic, season with ½ teaspoon salt, and cook, stirring occasionally, until softened and starting to brown, 6–8 minutes. Stir in 1 tablespoon chili crisp and scant ½ teaspoon white pepper, then remove from heat.
Transfer half of mixture to a blender and reserve other half in skillet. To skillet, add 12 ounces ground pork and ¾ teaspoon salt and cook over medium heat, breaking up with a wooden spoon, until browned, 4–5 minutes. Stir in remaining 1 tablespoon chili crisp, then grate 1½ ounces Manchego over top using a microplane (½ cup). Cook, without moving, until cheese melts, pork gets really brown and crisp on bottom, 6–8 minutes. Remove skillet from heat and let pork frico cool.
Season boiling water heavily with kosher salt; add 1 pound pasta and cook to al dente according to package directions. Reserve 1 cup pasta cooking water, then drain and add pasta back to pot.
While pasta cooks, add 1 can pumpkin, ⅓ cup cream, remaining 3 tablespoons butter, 1 tablespoon vinegar, ¼ teaspoon salt, and ¼ cup pasta cooking water to onions in blender and blend until smooth. Give it a taste and add more chili crisp if desired.
Pour blended sauce over pasta and toss to coat; add pasta cooking water, by ¼ cup, until sauce is loose and glossy (I use ¾ cup total*). Season to taste with salt (I usually add about ½ teaspoon).
Divide pasta between bowls. Using a firm metal spatula, scrap up large shards of crispy pork frico and serve over top pasta. Garnish with basil, if desired, and serve.