In a large bowl or stand mixer, stir butter well until very light and fluffy. A stand mixer works best.
Add in powdered sugar, stir until combined.
Add vanilla or lemon extract.
Slowly add in milk, one tablespoon at a time. Mix well as you add milk. If butter separates, slow your milk additions and be sure to increase stirring inbetween additions.
Stir after each addition of milk to see if it has reached a consistency that will pour. It will look thick, but a little runny.
Slowly drizzle over cake in a circular motion, making sure it evenly coats all sides. Use an offset spatula or butter knife to smooth out any lumps or uneven areas.
Pop cake in fridge and let set for 5-10 minutes.
Repeat icing drizzle step for a thicker more fondant like coat, then return to fridge. Repeat as needed.
If adding sprinkles or decorations, add them before setting, or they will not stick well.
If icing is too thin, add more powdered sugar. If too thick, more milk.