Warm a large skillet over medium heat. Once warmed, add 1 tablespoon olive oil, followed by the minced garlic and shallots. Sauté for about 2 minutes until very fragrant.
Add the pumpkin puree, cinnamon, nutmeg, salt, and pepper. Cook, stirring often, for about 5 minutes until it has deepened in color – this will deepen the pumpkin flavor.
Add the veggie broth and stir to combine. Bring to a simmer and cook until slightly thickened, about 5 minutes.
Add the heavy cream and stir to combine. Bring to a simmer and cook until slightly thickened, another 5 minutes.
Add the cooked pasta to the sauce and let it all come together for a few minutes, the residual starch from the pasta will finish thickening the sauce. If it gets too thick, use some reserved cooking water from the pasta to loosen it back up.