Preheat oven to 350°. Grease three 4" cake pans or one 6" cake pan with coconut oil and line with parchment rounds; set aside.
Melt coconut oil and then set it aside, allowing it to cool to room temperature.
In a large bowl, whisk the milk, pumpkin, syrup, and vinegar together, then add the cooled coconut oil.
In a separate bowl, stir the flour, baking soda, baking powder, cinnamon, and salt together.
Pour the dry ingredients into the wet, then use a rubber spatula or hand mixer to combine; it's ok if the batter is a little lumpy.
Pour the batter into the prepared cake pan(s), pounding on the counter a few times so the batter evens out.
Place pans into the oven and bake; 4" cake pan bake time: 27-32 minutes; 6" cake pan bake time: 40 minutes, or until a toothpick comes out clean. NOTE: if you're using 4" cake pans, it's easier to place them on top of a baking sheet so they don't accidentally spill.
Leave cakes in the pans for 10 minutes before carefully inverting them onto a cooling rack. Allow the cakes to cool completely before icing them.
For the icing, stir yogurt and syrup together. Once cakes have cooled, use a serrated knife to cut the tops of the cake off, and then ice the cake and layer it (alternatively, you can keep the layers separate if you want to have one layer for you, one for your pet and the third for someone else).
Optional: top cake with your dogs favorite foods, aka cheese, peanut butter or in my case, brussels sprouts. Enjoy this cake with your pup on their special day!