Preheat your oven to 350°F (175°C). Grease a 9×9 inch light metal cake pan and line it with parchment paper.

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

Cream together softened unsalted butter and granulated sugar with a hand mixer for about 2 minutes until pale and fluffy.

Add eggs one at a time, mixing well after each addition. Pour in vanilla extract and stir until smooth.

Blend buttermilk and canned pumpkin puree into the mixture until well combined.

Gradually add the dry ingredients to the wet mixture on low speed, being careful not to overmix.

Pour the batter into the greased cake pan and spread evenly. Bake for 35-38 minutes until a toothpick comes out clean.

Let the cake cool in the pan for 30 minutes, then transfer to a wire rack to cool completely.

Combine espresso, whole milk, sweetened condensed milk, pumpkin pie spice, and vanilla in a measuring cup to make the soak.

Beat softened butter until fluffy, mix in cold cream cheese, then gradually sift in the powdered sugar and instant espresso powder.

Once the cake has cooled, slice a thin layer off the top and poke small holes. Pour the latte soak over it and spread frosting.