Preheat your oven to 375°F. Line a small 11x17 baking sheet with parchment paper and plenty of grease; you don't want this cake to stick.
In a mixing bowl, sift together the flour, cocoa powder, and baking powder. Set this aside.
In your stand mixer, beat together the eggs and vanilla on high until foamy, about 4-5 minutes.
Add your sugar to the eggs about ¼ cup at a time, blending each time.
Add in the melted butter and mix well.
Mix in the dry ingredients and blend until they just come together.
Pour your batter in your baking sheet and spread evenly. You can tap this on the counter to help remove bubbles and spread it out.
Bake for 10-12 minutes, depending on how thick your batter was.
Spread out a dish towel on your counter and place your cooling rack on top of it, and then carefully flip the still-hot cake onto it. Remove the parchment paper and set it aside.
Dust the exposed top of the cake with cocoa powder. I used nearly ¼ cup, and brushed off the excess. Put the parchment paper back on top of the cocoa powdered side of the cake.
Carefully roll up your cake, keeping the parchment paper on top as a separating layer. Optionally, wrap your towel around this cake.
Allow the cake to cool for at least an hour.