Prep. Preheat oven to 350ºF. Line a baking sheet (17×12) with parchment paper and spray with nonstick baking spray or grease well with butter and dust with cocoa powder.
Mix dry ingredients. Whisk together flour, cocoa powder, baking powder, salt, and espresso powder in a medium mixing bowl.
Mix the wet ingredients. Beat the eggs with a whisk or an electric mixer until pale and thick. Then, mix in sugar and vanilla followed by the oil and milk until combined.
Combine the wet and dry ingredients. Slowly, mix in the flour mixture until well combined.
Bake the cake. Spread the cake batter in an even layer onto the prepared baking sheet and bake until the top springs back when touched about 10 to 12 minutes. Take care not to overbake.
Cool the cake. Remove the cake from the oven and let it cool for about 2 minutes. Loosen the bottom parchment with a knife. Top the cake with another piece of parchment paper and turn the cake out onto the new piece of parchment paper. Carefully remove the piece of parchment paper that the cake was baked on and discard it. Roll the cake into a loose roll and allow it to cool completely.