Start by spraying a 9 x 13-inch pan with non-stick cooking spray to ensure your cake releases easily once baked.
Preheat your oven to 350 degrees Fahrenheit, setting the stage for perfect baking.
In a large mixing bowl or a stand mixer, combine the dry ingredients: flour, sugar, cocoa, baking powder, baking soda, and salt. Mix them well to combine.
In a separate bowl or a large Pyrex measuring cup, whisk together the eggs, coffee, buttermilk, vegetable oil, and vanilla until smooth. The mixture should be well combined, creating a luscious batter.
Pour the wet mixture into the bowl of dry ingredients. Beat the mixture for a couple of minutes, scraping down the sides to ensure everything is well incorporated. The batter will be smooth and slightly thick.
Pour the cake batter into the prepared pan, smoothing the top for an even bake.
Place the pan in the preheated oven and bake for 30 to 40 minutes. Keep an eye on it; a toothpick inserted into the center should come out clean.
As the cake bakes, prepare the filling. In a microwave-safe bowl, combine sweetened condensed milk and chocolate chips. Microwave for 1 to 2 minutes, stopping to stir until the mixture is smooth and melted.
Once the cake is done, let it cool on a wire rack for about 5 minutes. Using the handle of a wooden spoon, poke rows of holes across the cake, creating spaces for the filling.
Pour the warm filling mixture over the holes in the cake, nudging it to ensure it fills the spaces adequately. Allow the cake to cool to room temperature before frosting.
For the frosting, beat together butter and cocoa until creamy. Add vanilla and mix well. Then, alternate adding milk and powdered sugar, mixing until smooth. Spread the frosting over the cooled cake, making it irresistible.