In a bowl, combine eggs, salt, and vanilla. Beat on high speed until they become foamy (should take you about a minute).
Add the granulated sugar to the beaten eggs and continue beating on high speed until the mixture doubles in volume and becomes lighter in color (should take around 2-3 minutes).
Add vegetable oil and buttermilk. Mix on low until well combined (you can switch to a hand-whisk at this point).
Sift in half of the flour mixture into the wet ingredients and slowly mix until combined. Then, sift in the remaining flour mixture and mix on low speed.
Add cooled coffee to the batter and gently combine until evenly distributed.
Grease a baking pan and pour the batter into it. Tap the pan lightly on the counter to release any air bubbles, and if desired, wrap the pan with baking strips (optional but recommended for even baking).
Preheat the oven to 165°C (325°F).
Place the prepared pan in the preheated oven and bake for approximately 45-50 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Once baked, transfer the pan to a cooling rack and allow the cake to cool completely at room temperature.