Preheat oven to 350 °F (177 °C) and line the bottom of a 9x13 inch with parchment paper and grease the sides of the pan. Set aside.
In a large bowl, whisk together flour, sugar, baking powder, baking soda, pumpkin pie spice, and salt.
In the bowl of a stand mixer, combine Greek yogurt (or vegetable oil) and pumpkin puree. Mix in eggs one at a time, making sure each egg is well incorporated after each addition.
Add the flour mixture to the stand mixer in 3 additions, mixing well after each addition.
Evenly spread batter into prepared pan and bake for 25-30 minutes, or until toothpick inserted into the center comes out clean.
Let cake cool completely before frosting.
To make the frosting, combine all the frosting ingredients in a bowl and whisk until all is incorporated. You'll want the frosting to be thick, but not too thick that you can't pour it. If you feel you need more liquid, add additional milk 1 tbsp. at a time.
Once cake has completely cooled, pour the frosting all over the top of the cake and spread out evenly with an offset spatula. Let sit for 10-15 minutes to harden then slice to serve.
Store cake in an airtight container for up to one week.