Preheat oven to 350 F. Line 2 large baking sheets with silicone baking mats.
In a large mixing bowl, beat butter and sugars together until well-combined.
Mix in vanilla.
Add in eggs one at a time, and mix in until combined.
Stir in the flour, cocoa, baking soda, and salt until just incorporated.
Drop by 1.5 tablespoon scoops (medium cookie scoop) 2 inches apart on the prepared baking sheet.
Bake 10 minutes.
Cool on baking sheet for 2 minutes before removing to a wire rack.
To make the frosting, add cocoa powder, hot water, melted butter, and vanilla to a large bowl.
Mix together until combined.
Whisk in the powdered sugar until combined.
Spread frosting over room temperature cookies.
Notes
"Cool room temperature" means that the butter should dent slightly when pressed. If it doesn't dent when pressed, it's too cold. If it smooshes, it's too warm.
Be sure to properly measure the flour to avoid dry, crumbly cookies. Either Sift or stir the flour, lightly spoon into the measuring cup, and then level off.