Preheat the oven to 350 degrees F. Line a 9-inch cake pan with parchment paper. Oil the sides lightly. 

In a medium bowl, whisk pumpkin puree, oil, yogurt, sugar, and vinegar.

In a large bowl, combine baking powder, baking soda, cinnamon, nutmeg, optional pumpkin pie spice, flour, and salt. Slowly pour wet into dry, folding to combine. Try not to over-mix, just combine until there are no visible flour spots. 

Pour mixture into prepared cake pan and tap the pan on the counter to release any air bubbles. Bake on the center rack for 50-65 minutes, until a tester (like a toothpick) stuck inside the cake comes out clean (without any crumbs). 

While cake is cooling, prepare frosting by melting butter in a skillet on the stove. To brown it, cook over medium heat until the water inside starts to evaporate and it smells nutty. This normally takes 5-7 minutes. You should see little brown pieces forming. Remove from heat and let cool. Add in powdered sugar, vanilla vanilla, almond milk, and cinnamon. Stir to combine and chill until ready to use.

Using a spatula, frost the cake once it is completely cool. Store cake on the counter, covered, for 3-5 days.