Add the walnuts to a large dry pan over medium low heat. Cook until toasted, stirring often so they don’t burn. Set the walnuts aside and return the pan to the heat.
Up the temperature to medium high heat and melt the butter. Stir in the garlic and cook until golden brown. Add in the white wine and cook until reduced by half. Scrape up any stuck on bits with a wooden spoon and add in the vegetable stock.
Bring the vegetable stock to a boil then add in the linguine. Stir immediately and often to keep the noodles from sticking together. Cook to al dente according to package directions.
Add the pumpkin puree and triple-creme brie to the sauce and cook until the brie is melted. Stir in the spinach and cook until it is only just wilted. Season with salt and black pepper to taste.
Serve with chopped walnuts and parmesan cheese on top.
This pasta will stay good refrigerated up to 5 days. If you want to serve this pumpkin pasta with a side dish, it goes well with a light salad, baked chicken, sausages, or roasted root vegetables.