Step 1
Heat the oven to 450 degrees. On a sheet pan, mash together the butter and miso. Add the garlic and squash, drizzle with 1 tablespoon olive oil, and toss to coat with the miso-butter mixture. Sprinkle 1 teaspoon salt and season with pepper. Cook until easily pierced with a fork and the raw taste is gone, 25 to 30 minutes.
Step 2
Meanwhile, bring a large pot of salted water to a boil. Add the pasta, adjusting the heat to maintain a gentle boil, and cook until just shy of al dente. Reserve 1 cup pasta water, then drain the noodles. If done before the squash, drizzle with olive oil to prevent the noodles from sticking together. Leave in the sink to drain.
Step 3
When the squash is done, return the pasta to the pot over low heat. Scrape in squash, garlic and any liquid that accumulated, then add the Parmesan and ½ cup pasta water, stirring well until the noodles have a light sheen to them. If it appears dry, add more pasta water a tablespoon at a time until you reach your desired consistency. Stir in the lime zest and juice, season to taste with salt, and top with pepper and red-pepper flakes, if using. Serve with extra cheese.