Step 1: Bake the Pumpkin Cake

1. Preheat the oven to 350°F (175°C). Grease a 9×9 inch light metal baking pan and line it with parchment paper.
2. In a medium bowl, whisk together the flour, pumpkin pie spice, baking powder, baking soda, and salt. Set aside.
3. In a large bowl, cream the butter and sugar together for 2 minutes with an electric mixer.
4. Add the eggs and vanilla and mix on medium speed until smooth and pale (about 1 minute).
5. Mix in the buttermilk and pumpkin puree on medium-low speed until combined (it may look curdled).
6. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until combined.
7. Pour the batter into the prepared pan and bake for 35–38 minutes or until a toothpick inserted in the center comes out clean.
8. Cool the cake in the pan for 30 minutes, then transfer it to a wire rack to cool completely.

Step 2: Prepare the Latte Soak

1. In a liquid measuring cup, mix together the espresso, milk, sweetened condensed milk, pumpkin pie spice, and vanilla extract. Set aside.

Step 3: Make the Cream Cheese Frosting

1. In a large bowl, whip the butter on high speed until pale and fluffy (about 5–10 minutes).
2. Add the cold cream cheese and mix on medium speed until combined.
3. Sift the powdered sugar into the mixture in batches, mixing on low speed until incorporated, then on high speed for 1 minute until fluffy.
4. Dissolve the instant espresso powder into the vanilla extract and mix it into the frosting along with the pumpkin pie spice until smooth and fluffy.

Step 4: Assemble the Cake

1. Cut a thin layer off the top of the cooled cake for better soak absorption.
2. Poke holes into the surface of the cake using a wooden stick or spoon handle.
3. Slowly pour the latte soak over the cake, letting it absorb gradually.
4. Frost the cake generously with the espresso cream cheese frosting using an offset spatula for an even layer.
5. Sprinkle with additional pumpkin pie spice for decoration.
6. Slice into 16 pieces and serve.