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.
1 cup butter, ¾ cup granulated sugar, ½ cup brown sugar
Mix in vanilla.
1 teaspoon vanilla
Add in eggs one at a time, and mix in until combined.
2 large eggs
Stir in the flour, cocoa, baking soda, and salt until just incorporated.
2 ½ cups all-purpose flour², ⅔ cup unsweetened cocoa powder, 1 teaspoon baking soda, ½ teaspoon kosher salt³
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.
⅓ cup unsweetened cocoa powder, ⅓ cup hot water, ¼ cup butter, 1 teaspoon vanilla
Mix together until combined.
Whisk in the powdered sugar until combined.
3 cups powdered sugar
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.