Preheat your oven to 350°F (175°C) and prepare a 9x9 inch baking pan with butter or cooking spray and parchment paper.

In a medium bowl, whisk together the dry ingredients: flour, pumpkin pie spice, baking powder, baking soda, and salt.

In a large mixing bowl, cream together softened butter and granulated sugar until light and fluffy.

Add eggs one at a time to the butter-sugar mixture, mixing well after each addition, then mix in vanilla extract.

Beat in buttermilk and pumpkin puree until just combined.

Gradually fold the dry mixture into the wet ingredients until combined. Do not overmix.

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

While the cake cools, whisk together brewed espresso, whole milk, sweetened condensed milk, pumpkin pie spice, and vanilla for the soak.

In another bowl, beat softened butter until fluffy, then mix in cream cheese, powdered sugar, and instant espresso until smooth for the frosting.

Once cooled, poke holes in the cake and pour the latte soak over it, then frost the top and sprinkle with pumpkin pie spice.

Slice the cake into 16 pieces and serve.