Heat the butter and oil in a heavy - bottomed stockpot, add the onions, and cook over medium - low heat for 10 minutes, or until translucent. Add the pumpkin puree, butternut squash, chicken stock, salt, and pepper. Cover and simmer over medium - low heat for about 20 minutes, until the butternut squash is very tender. Process the mixture through the medium blade of a food mill. Return to the pot, add the half - and - half, and heat slowly. If the soup needs more flavor, add another teaspoon of salt. Serve hot with garnishes, if desired.
Cook's Note: To serve with croutons, remove the crusts from 2 slices of white bread, cut them in 1/2-inch cubes, and saute them in 1 tablespoon of butter until browned. Season with salt and pepper.