Set out all butter to softened. Crack the eggs into a bowl so they can warm to room temperature. Preheat the oven to 350 degrees F. Butter a large 15 1/2x10 1/2-inch deep-sided jelly roll pan. (This is sometimes called a XL baking pan or roasting pan.) Then sprinkle the pan with flour to coat the bottom and sides. Shake the pan, then dump out the excess flour.
Stir the bag of flour well before measuring. In a medium bowl, mix the flour, pumpkin pie spice, baking powder, baking soda, and salt together.
Place the butter and both sugars in the bowl of an electric stand mixer. Cream the butter until light and fluffy. Start on low speed, then move up to high and allow the butter mixture to beat for 4-5 minutes until the sugar crystals are breaking down into the butter. (This is KEY to a light fluffy cake texture.)
Scrape the bowl with a spatula. Then beat in the eggs one at a time. Scrape the bowl again. Then turn the mixer on low and alternate adding the flour mixture and the pumpkin puree until both are combine. Once the batter is smooth, turn off the mixer.
Scoop the batter into the prepared pan and smooth it out evenly. Bake for 45-50 minutes, until the center is puffy and a toothpick inserted into the middle comes out clean. Do not open the oven until the timer goes off.
Cool the cake completely before you continue. You can place it in the refrigerator to speed up cooling time.
For the Buttermilk Frosting:
Place the softened butter in the bowl of a stand mixer, with a whip attachment. (Make sure to clean the bowl.) Whip on high until very fluffy and soft. Then turn the mixer on medium-low and mix in the buttermilk, vanilla, and salt.
Slowly add the powdered sugar, one cup at a time, until five cups are incorporated. Turn the mixer on high to whip out all the clumps. Once the frosting is light and smooth, check the consistency. If needed, add another 1/2 to 1 cup powdered sugar. Scrape the bowl and whip again until smooth.
Spread the frosting over the top of the cooled pumpkin spice cake. Sprinkle with extra pumpkin pie spice or cinnamon. Cut into 32 pieces. Cover until ready to serve.
Cake tastes (and feels) best when left at room temperature. This cake can sit out at room temperature for up to 4 or 5 days. To keep longer, cover well and refrigerate for up to 2 weeks. Then allow it to warm to room temperature before serving.