Preheat the oven to 350°F. Grease two 9x5-inch baking pans with flour-based baking spray (or grease and flour pans).
Cream the butter and sugar together in the bowl of an electric mixer. With the mixer running, add the eggs one at a time. Mix in the vegetable oil, vanilla extract and pumpkin puree. Scrape down the bowl and mix again briefly.
Add the flour, salt, soda, cinnamon and nutmeg to the butter mixture. Mix well on low speed until just combined. Using a large rubber spatula scrape down the bowl and mix again until well combined. Fold in the walnuts.
Divide the batter between the prepared loaf pans and bake for 45 minutes to1 hour. Loaves are done with they are well-browned and a toothpick tester inserted in their centers comes out clean.
Turn the loaves out onto wire cooling racks. Serve slices warm or at room temperature.
Store loaves in large zip-top bags with the air removed, or double wrapped in plastic wrap.