Inspired by Starbucks' cult-classic harbinger of fall itself - the pumpkin spice latte - this cake buzzes with two glorious layers of coffee-tinged pumpkin cake sandwiching an espresso cream cheese filling, and then it's topped off whipped cream and a sprinkling of nutmeg.
Preheat oven to 350 degrees Fahrenheit. Position rack in the center of the oven. Butter two 8-inch cake pans and line the bottom with parchment paper.
In a large bowl, sift together the flour, baking powder, baking soda, cinnamon, ginger, allspice, nutmeg, cloves, and salt.
In the bowl of a stand mixer fixed with the paddle attachment, beat together the oil, granulated sugar, and dark brown sugar on low until blended. Add the eggs one at a time, beating well after each addition. Add the pumpkin puree, espresso powder, and vanilla extract and beat on medium until combined.
With the mixer on low, slowly add the flour mixture to the wet ingredients, beating just until incorporated. Remove bowl from mixer and stir once or twice with a wooden spoon to ensure the batter is well-combined.
Divide the batter between the two prepared cake pans. Smooth the tops with an offset spatula.
Bake for about 35-40 minutes or until a toothpick inserted in the center of the cakes comes out clean.
Place on wire racks and let cool for about 10 minutes. Carefully loosen the sides of the cake by running a butter knife around the edge of the pans. Invert the cakes onto wire racks and remove the parchment paper. Let cool completely.
Make the filling
In a small bowl, stir together the instant espresso powder and the hot water until all the powder is dissolved. Let cool.
In the bowl of a stand mixer with the whisk attachment, add the cream cheese, powdered sugar, whipped cream, vanilla extract, and espresso mixture.
Beat on medium until smooth, thick, and forming soft peaks, about 1 minute.
Make the whipped cream topping
In the bowl of a stand mixer with the whisk attachment, add the whipping cream. Beat on low until the mixture begins to thicken, then increase speed to medium high. As the mixture thickens, add the vanilla and sugar. Continue beating until stiff peaks form, about 1 minute.
Assemble the cake
Place one cake layer on a cake plate, right side up. Scoop the espresso cream filling onto the top of the layer and, using a spoon, smooth to about 1/2 inch from the edge.
Carefully place the second layer upside-down on top of the filling.
With a large spoon, pile the whipped cream on the top of the cake, covering the entire top of the cake.
Sprinkle with fresh grated nutmeg.
Serve within two hours; otherwise the cake should be refrigerated.