Pour the butter into the bowl of an electric mixer fitted with the paddle attachment. Mix in the sugar on medium speed until thoroughly combined.
Add the flour and cocoa powder mix until thoroughly combined.
Add the egg whites slowly. Mix until a homogenous paste is obtained.
Refrigerate until firm, because it will be easier to spread when cold.
Spread 20g / .71oz of the batter in a 10cm / 4in circular stencil on a nonstick rubber mat with a small offset spatula. Repeat until the nonstick rubber mat is filled with circles (about 12 circles per mat), leaving 2.5cm / 1in between each circle.
Bake until firm, about 6 minutes. Shape around a metallic cornet mold 10cm / 4in long by 3.75cm / 1.5in diameter while hot. If the cones cool off and become too firm to shape around the tube, return the sheet pan with the cones to the oven to soften them. Repeat with the remaining batter.
Reserve the finished cones in an airtight container at room temperature. Discard after 2 days.