Preheat oven to 350°F. Melt butter, water, and cocoa. Mix sugar, eggs, and vanilla, then add cocoa mixture. Stir in flour, baking soda, salt, and milk. Scoop dough and bake 8–10 minutes. Prepare icing by melting butter, cocoa, and milk, then whisk in powdered sugar and vanilla. Spoon icing over warm cookies.
Notes
Ice cookies while warm for best texture. Do not overbake.