For the Coffee Cake:

1. Preheat your oven to 350 degrees Fahrenheit. Grease three 6-inch cake pans with non-stick spray and line the bottoms with parchment paper rounds.
2. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
3. In a large mixing bowl, cream together the butter and sugar until light and fluffy.
4. Dissolve the instant coffee in the vanilla extract. Add the eggs and the vanilla/instant coffee mixture to the butter mixture and mix until smooth.
5. Alternate adding the dry ingredients and the buttermilk to the butter/coffee mixture, mixing until just combined.
6. Fold in the shredded carrots until evenly distributed.
7. Divide the batter evenly among the prepared cake pans and bake for 27-31 minutes, or until a toothpick inserted into the center comes out clean. Let cool completely.

For the Coffee Buttercream:

1. In a large bowl, whip the butter and salt until pale and fluffy.
2. Gradually sift in the powdered sugar until combined.
3. Dissolve the instant coffee in the vanilla extract. Add it to the frosting and mix until combined.
4. Whip the frosting until light and fluffy.

For the Coffee Ganache:

1. Heat the heavy cream and instant coffee until the coffee is dissolved.
2. Add the chopped white chocolate and coffee/cream mixture to a double boiler. Heat until melted together.

Assembling the Cake:

1. Apply a thin layer of frosting (crumb coat) to the cake layers and chill for 30 minutes.
2. Apply the final coating of frosting and chill for another 30 minutes.
3. Pour the coffee ganache drip around the top edges of the cake and smooth it out.
4. Pipe decorative swirls of frosting on top of the cake. Decorate with espresso beans and a dusting of cocoa powder.
5. Serve and enjoy with a cup of coffee!