Cook the pasta according to the package instructions. The sauce can be made entirely while the pasta cooks.
If you wish to top with toasted walnuts, ensure they are chopped small and place in a small skillet on medium-low heat. Let them sit, shaking every few minutes, while you make the sauce. Once they start to darken and are fragrant, remove from heat.
Warm the olive oil in a pan on medium heat. Add the garlic and sauté for 1-2 minutes until lightly browned, then add the tomato paste and cook for another 1-2 minutes. Be careful not to let the garlic burn.
Add the pumpkin purée, dairy-free milk, and vegetable broth to the pan. Season to taste with salt and pepper, and add a pinch of nutmeg for spice. Whisk to combine and cook for another 3-5 minutes, turning the heat to low.
When almost ready to serve, add the spinach if you wish and cook for 2 minutes until wilted.
Drain the pasta and add it to the pan. Cook in the sauce for 1 minute.
Top with toasted walnuts and (vegan) parmesan or nutritional yeast. Enjoy!