Creating this Simple Pumpkin Spice Latte Cake involves several easy steps:

1. Preheat Oven: Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
2. Mix Dry Ingredients: In a large bowl, whisk together the flour, sugar, baking powder, baking soda, salt, and pumpkin pie spice.
3. Combine Wet Ingredients: In another bowl, mix the pumpkin puree, eggs, vegetable oil, vanilla extract, and cooled coffee until well combined.
4. Combine Mixtures: Gradually add the wet ingredients to the dry ingredients, stirring until just combined. Take care not to overmix.
5. Divide Batter: Pour the batter evenly into the prepared cake pans.
6. Bake: Bake for 30-35 minutes or until a toothpick inserted in the center comes out clean.
7. Cool: Remove the cakes from the oven and let them cool in the pans for about 20-25 minutes. Then, transfer them to a wire rack to cool completely.
8. Make the Frosting: In a medium bowl, beat the softened butter until creamy. Gradually add the powdered sugar, cooled coffee, pumpkin pie spice, and vanilla extract. Beat until smooth and fluffy.
9. Assemble: Once the cakes are completely cool, spread a layer of frosting on top of one cake layer. Place the second layer on top and frost the top and sides as desired.
10. Decorate: Optionally, decorate with cinnamon, chocolate shavings, or finely chopped nuts to enhance presentation.

Follow these simple steps to create an incredibly moist and flavorful cake that embodies the spirit of pumpkin spice.