Start by mixing your cold milk and cream in a glass. If you're using a 5-ounce glass, mix 90ml of cold milk with 30ml of cream. For a bigger 8-ounce glass, use 120ml of milk and 50ml of cream. Put this mixture in the freezer for a few minutes to get it really cold.
While your milk is chilling, grind your coffee beans. You'll need 18 grams of beans, ground a bit finer than regular espresso. This will give you the best flavor. Press the grounds firmly with your tamper.
Get your cold glass ready. Take your milk mixture out of the freezer and pour it into the glass, leaving some room at the top for the espresso.
Now make your espresso shot. This should take between 30 to 50 seconds to pull. The slower extraction gives you better flavor.
Here's the most important part: very slowly pour your hot espresso over the cold milk. Pour it gently so it creates nice layers. You'll see the espresso make beautiful swirls in the milk – that's exactly what you want.
Serve your Dirty Coffee right away, before the temperatures start to mix too much. Don't stir it – the layers are part of what makes this drink special.