Cook the pasta al dente (it should have a bite to it, don't overcook the pasta). Drain and set aside.
Melt the butter in a large pot. Make brown butter: cook the butter over medium-low heat until it smells nutty and it's light golden brown in color (about 1-2 minutes).
Add the flour, whisk until well-combined then cook for 1 minute. Whisk it from time to time making sure it doesn't get too dark.
Add pumpkin puree, cinnamon, nutmeg, mustard, and garlic powder. Bring to a boil, then cook for 2 minutes, whisking often, until the puree is thickened a bit. Allow it to brown a little bit at the bottom of the pot but be careful not to burn it.
Slowly add milk, whisking constantly, until well-combined. Bring to boil and cook for 2-3 minutes, whisking from time to time, making sure the sauce doesn't burn at the bottom of the pot.
Take the pot off the heat, make sure the sauce is not bubbling when you add all kinds of cheese. Gradually add the cheese, about 1/2 cup at a time, whisking vigorously after each addition. Add the next portion of cheese when the previous one has been incorporated/fully melted. Grated cheese will melt the easiest but you can also get away with small chunks. If the cheese is not melting you can put the pot back on the burner and heat it gently over low heat.
Season your cheese sauce with salt, pepper, and cayenne pepper to taste.
Add the cooked pasta and stir until combined. The dish will be rather runny at this point but it will thicken considerably while cooling.
Enjoy!