Preheat oven to 350 and line with cupcake liners. In a bowl, whisk together the oil, eggs, pumpkin, sugar, brown sugar and vanilla until smooth. In another bowl whisk together the flour, salt, baking powder, baking soda and spices. Add the dry ingredients to the wet and mix gently until combined.
In another clean bowl, whisk the cream cheese, sugar, vanilla and flour until smooth. You can do this in a stand mixer, or I used a little hand held blender wand to be sure it was smooth.
Divide the pumpkin mix into the 12 muffin wells and using a cookie scoop or 2 spoons, put a golf ball sized dob of cream cheese in the center. It will settle in as it cooks. Bake for 10 minutes, rotate the pan and bake 10 more minutes. Keep an eye on them for doneness and check by inserting a toothpick into the pumpkin portion as close to the center as you can without going through the cream cheese. When it comes out clean they are done.
Cool for 10 minutes then remove from the pan.