Peel ½ small butternut squash (about 1¼ lb.) and cut flesh into ½" cubes. Peel and finely chop 1 onion. Using the flat side of your chef’s knife, crush 1 garlic clove, then peel and finely chop. Coarsely chop 1 cup kimchi (some kimchi juice is okay; no need to drain). Heat 2 Tbsp. extra-virgin olive oil in a large Dutch oven or other heavy pot over medium-high. Add onion and cook, stirring often, until softened slightly, about 2 minutes. Add garlic and kimchi and cook until kimchi is starting to brown and stick to bottom of pot, about 5 minutes. Add squash to pot and reduce heat to medium. Cover and cook, stirring halfway through, until squash is tender (a paring knife should pierce flesh easily), 6–8 minutes. Remove lid and stir in 1 lb. elbow macaroni, shells, cavatappi, rigatoni, or other short pasta, along with 4 cups vegetable stock or water. If using water, add 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt (if you broth isn't very flavorful, you may want to add a bit of salt too; start with 1/2 tsp. Diamond Crystal or 1/4 tsp. Morton kosher salt). Cover and bring to a simmer; cook until pasta is al dente and most of stock is absorbed (you want some starchy liquid left in pan), 6–8 minutes. Meanwhile, grate 1 lb. sharp cheddar on the large holes of a box grater. Trim and finely slice 4 scallions. Reduce heat to low and add cheese to pot; stir until cheese is melted and gooey, about 2 minutes. Season mac and cheese with a few grinds of freshly ground black pepper and scatter scallions over.