Preheat the oven to 350?F. Grease a 9?9 inch light metal baking pan and line it with parchment paper.

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

In a large bowl, cream together the softened butter and granulated white sugar for 2 minutes with an electric mixer on high speed.

Add in the eggs and vanilla extract, mixing on medium speed until pale in color and smooth, about 1 minute.

Mix in the buttermilk and canned pumpkin puree on medium-low speed until combined.

Add the dry ingredients to the wet ingredients and mix on low speed until fully combined. Scrape the sides of the bowl as necessary.

Pour the batter into the prepared baking pan. Bake for 35-38 minutes, or until a toothpick comes out clean from the center.

Let the cake cool in the pan on a wire rack for 30 minutes, then release it from the pan to cool completely on the rack.

While the cake cools, mix together the espresso, whole milk, sweetened condensed milk, pumpkin pie spice, and vanilla extract to make the latte soak.

In a large bowl, whip the softened butter on high speed until pale and fluffy, about 5-10 minutes.

Add the cold cream cheese and mix on medium speed until combined and fluffy.

Sift in the powdered sugar gradually and mix on low speed until combined, then on high speed for 1 minute until fluffy.

Dissolve the instant espresso powder in the vanilla extract in a small ramekin. Add to the frosting along with the pumpkin pie spice and mix until combined and fluffy.

When the cake is completely cooled, cut a thin layer from the top of the cake to help absorb the latte mixture. Poke holes in the top of the cake.

Slowly pour the latte mixture over the cake, allowing it to absorb.

Frost the top of the cake with a thick layer of espresso cream cheese frosting and sprinkle pumpkin pie spice on top. Cut into 16 slices and serve.