Preheat oven to 350°F.
Grease and flour two square 8x8” baking pans. You can line the pans with circles of parchment for easier removal. (If you only have one square pan, you can bake one cake and cut it into two layers when cooled.)
Combine vinegar and milk and set aside to curdle.
Whisk dry ingredients together in a mixing bowl.
In a separate bowl, combine all wet ingredients. Add wet mixture to dry ingredients and stir until smooth.
Divide cake batter between the two prepared baking pans, and bake for 25-30 minutes, or until a knife inserted into the center comes out clean and the cake springs back when gently pressed. (If you’re using only one cake pan, this may take up to 40-45 minutes.)
Remove and cool for 10 minutes in pans, then transfer to wire rack to cool completely.
If you have time to make the cake the night before, you can leave it out overnight to get slightly stale. It will be able to absorb more of the coffee soak this way, but it's optional.