Preheat oven to 350°F (175°C). Spray a 9 x 13-inch pan with non-stick cooking spray and set it aside.
From the measured ingredients, set aside the following for the poke filling/glaze: 1/4 cup of the cooled coffee, 1/4 cup of the buttermilk, 2 tablespoons sugar, 2 tablespoons unsweetened cocoa, and 1/4 teaspoon vanilla. (Keep the reserved portions separate and use the remaining listed ingredients for the cake batter.)
In a large mixing bowl, whisk together the dry ingredients: flour, the remaining sugar, the remaining cocoa, baking powder, baking soda, and salt until evenly combined.
In a separate bowl, whisk the wet ingredients: the eggs, the remaining coffee (all coffee minus the reserved 1/4 cup), the remaining buttermilk (all buttermilk minus the reserved 1/4 cup), vegetable oil, and the remaining vanilla (total vanilla minus the reserved 1/4 tsp) until smooth.
Pour the wet ingredients into the dry ingredients and beat on medium speed (or whisk by hand) for about 1–2 minutes until the batter is uniform, scraping down the sides of the bowl as needed.
Pour the batter into the prepared 9 x 13-inch pan and smooth the top. Bake in the preheated oven for 30–40 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Remove the cake from the oven and let it cool in the pan on a wire rack for about 5 minutes.
Using the handle end of a wooden spoon (or similar), poke rows of holes across the warm cake, spacing them about 1 inch apart so the cake is well-perforated.
Make the poke filling/glaze: in a small bowl whisk together the reserved 1/4 cup coffee, reserved 1/4 cup buttermilk, reserved 2 tablespoons sugar, reserved 2 tablespoons cocoa, and reserved 1/4 teaspoon vanilla until smooth. If the sugar or cocoa are slow to dissolve, warm the mixture briefly (10–20 seconds) in the microwave and whisk again until smooth.
Pour the glaze evenly over the top of the cake, letting it sink into the holes. Reserve any leftover glaze to spread on top.
Cool the cake to room temperature (about 45–60 minutes). If there is any reserved glaze, spread it over the cooled cake before serving.
Cut into slices and serve.