In a medium saucepan, combine the blueberries, granulated sugar, and lemon juice over medium heat. Stir until the berries begin to release their juices. Add the cornstarch slurry (cornstarch mixed with water), and continue cooking, stirring constantly, until the mixture thickens, about 4–6 minutes. Remove from heat. Let it cool. Reserve ½ cup of this compote for the frosting.

Preheat your oven to 350°F (175°C). Grease and line two 9-inch round cake pans with parchment paper.

In a large mixing bowl, sift together flour, cocoa powder, sugar, baking powder, baking soda, and salt.

In a separate bowl, whisk together the eggs, milk, sour cream, oil, and vanilla extract until smooth.

Pour the wet mixture into the bowl with the dry ingredients. Mix just until combined. Then slowly pour in the hot coffee (or water), mixing gently until the batter is smooth and thin.

Divide the batter evenly between the prepared pans. Bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean. Remove from oven and let the cakes cool in the pans for 10 minutes, then turn them out onto a cooling rack to cool completely.

In a mixing bowl, beat the softened cream cheese and butter until creamy and smooth. Add in the reserved ½ cup of blueberry compote and mix until well combined. Gradually add powdered sugar, beating until fluffy and your desired consistency is reached.

Once the cake layers are completely cooled, use a serrated knife to level the tops if needed. Place the first cake layer on a serving plate. Spread a layer of blueberry filling over it (about ½ cup or more), spreading evenly but not too close to the edges.

Place the second cake layer on top. Use the blueberry cream cheese frosting to frost the top and sides of the cake. Use an offset spatula for a smooth finish, or create a rustic, swirled look.

Refrigerate the cake for at least 30 minutes before slicing to help it set. Serve chilled or at room temperature. Garnish with fresh blueberries or chocolate shavings if desired.