In a large mixing bowl, whisk together the sugar, vegetable oil, pumpkin puree, baking soda with water, vanilla extract, cinnamon or pumpkin pie spice, and salt until well combined. Add the eggs to the mixture, whisking until well incorporated.
Pour the batter into the prepared pan, and gently tap it a couple of times on the counter to remove any air bubbles. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely.
In a separate large bowl, cream together the butter and cream cheese on medium speed with an electric hand mixer until well blended, about 2 minutes. Add in the vanilla extract and salt, mixing again.