Preheat the oven to 350°F. Grease a 9×9 pan and line it with parchment paper.

In a medium bowl, whisk together the flour, pumpkin pie spice, baking powder, baking soda, and salt. Set aside.

In a large mixing bowl (or stand mixer), cream the butter and sugar until light and fluffy, about 2 minutes.

Add the eggs one at a time, then the vanilla. Mix until smooth and pale.

Mix in the buttermilk and pumpkin purée.

Add the dry ingredients and mix on low until just combined. Scrape down the bowl as needed.

Pour the batter into your prepared pan and bake for 35–38 minutes, or until a toothpick comes out clean.

Cool in the pan for 30 minutes, then lift out with the parchment and let cool completely on a rack.

In a small bowl or liquid measuring cup, whisk together the espresso, milk, sweetened condensed milk, pumpkin pie spice, and vanilla.

Beat the butter on high speed until light and fluffy, 5–7 minutes.

Add the cold cream cheese and mix until smooth.

Sift in the powdered sugar, a little at a time, mixing on low until incorporated. Turn the mixer up to high for 1 minute.

Dissolve the espresso powder into the vanilla, then add it to the frosting along with the pumpkin pie spice. Mix until fluffy.

Once the cake is completely cooled, trim a thin layer off the top so the latte soak can absorb better. Place on a serving platter.

Use the handle of a wooden spoon (or even a honey dipper) to poke holes all over the cake.

Slowly pour the latte mixture evenly over the cake, letting it soak in.

Spread a generous layer of frosting over the top.

Sprinkle with a little pumpkin pie spice, slice into squares, and serve!