Cook linguine to al dente according to the instructions on the package. The pasta will cook a bit more when added to the sauce.
Melt butter in a large saucepan over a medium heat. Add garlic and cook for 30 seconds. Add half-and-half and pumpkin puree. Whisk until well combined.
Stir in parmesan cheese, basil, sea salt and white pepper and continue cooking for 5 to 10 minutes until the sauce heated through and begins to thicken slightly. Add pasta (and chicken, if using) and cook for another 5 minutes.
Serve immediately. Top with shredded parmesan cheese and crushed red pepper flakes, as desired.