Preheat the oven to 350°F / 180°C and prepare two 8-inch cake pans.
In a stand mixer, cream together the butter and both sugars until combined.
Add the eggs, one at a time, beating after each addition.
Mix in the pumpkin puree and vanilla, don't worry if the batter looks curdled after adding the pumpkin, it will come back together when we add the flour.
In a large bowl, sift together the remaining dry ingredients and mix.
Add half of the flour mixture to the pumpkin batter and mix it in slowly.
Pour in the milk and oil, then mix until incorporated.
Add the remaining flour mixture and mix on low speed until incorporated.
Divide the batter between the prepared cake pans and bake for 35-40 minutes, or until a skewer inserted into the middle of the cakes comes out clean.
If you want to add the pumpkin curd as a filling inside the cake, make sure you make it early enough that it has time to cool before you fill and frost the cake. You can find instructions on how to make the pumpkin curd recipe here.
Make the Cinnamon Cream Cheese Frosting
Beat the room-temperature butter until creamy. Add the cream cheese and beat them together until combined and smooth.
Sift in the powdered sugar and mix in very slowly, then turn up the speed to medium and beat for 1 minute.
Add the vanilla and cinnamon and beat for another minute.
Assemble and Decorate
Once the cakes have completely cooled, remove them from the cake pans and use a cake leveler or serrated knife to cut the tops off so they are totally flat.
If you want 4 thin layers like I have in the pictures, cut each cake layer in half. This is optional, you can just have two thicker layers if you like.
Stack the cake layers, filling an even layer of cinnamon cream cheese frosting in between as you go.
If you are adding the pumpkin curd, add it to the middle layer. Pipe a ring of cream cheese frosting around the outer border of the cake first to stop the pumpkin curd from leaking out the side. Fill in with curd and then continue stacking your cake as normal. You could also put pumpkin curd in every layer if you wanted to, this recipe makes enough curd for that.
Once you are done stacking, cover the whole cake in a thin layer of cream cheese frosting and decorate however you like.
If you want to achieve the pumpkin swirl as I have in the pictures, Spread a layer of cream cheese frosting all over the top of the cake, then add a dollop of pumpkin curd in the middle. Use a palette knife or spatula to create a swirl by holding it still on the cake while you turn the cake on a turntable or plate and slowly moving the spatula outwards.
Notes
If you want to add the pumpkin curd filling, make a batch of my pumpkin curd recipe in advance. The recipe makes more curd than you will need for this cake, so you'll have som left over. You can keep it in the fridge for 1-2 weeks and use for other desserts or as a topping for pancakes or ice cream. Make sure you use pumpkin puree and not pumpkin pie filling.