Preheat oven to 350 degrees and butter/flour an 8 inch pan (for a slim cake) or a 6 inch pan for a higher cake
Beat the butter till creamy, about 2-3 minutes.
Add the sugars and beat for another 2-3 minutes until the sugars are fully incorporated and the mixture starts to look nice and fluffy.
Now add the eggs one by one, beat 1 minute after each addition, and now mix in your vanilla extract.
Then sift half your flour mix in, mix, scrape sides with a spatula, add remaining liquid (coffee solution and milk) and then sift in the other half of the flour mix, beat till combined.
Now start checking on it after the 30 minute mark, that’s around when the cake should be done ( a toothpick inserted in the center comes out clean) if you are using an 8 inch pan. With a 6 inch, it takes 12-15 minutes longer.
Whip the butter till fluffy, then add the powdered sugar gradually and at low speed till incorporated and finally add in your coffee mix, vanilla, and salt. Beat well.
Please note that the frosting just covers the top of an 8 inch cake and not the sides!