Spray a 15 x 10 x 1 in. (37 x 25 x 3 cm) jelly-roll pan; line the bottom with wax paper; spray the paper.
Sift the flour, cocoa, and baking powder together.
With an electric mixer, beat the eggs in a medium bowl until thick and creamy and light in color.
Gradually add the sugar and acesulfame-K, beating constantly until the mixture is very thick.
Stir in the coffee and vanilla extract.
Fold in the flour mixture.
Spread the batter evenly in a prepared pan.
Bake in a 350°F (180°C) oven for 12 minutes or until the center springs back when pressed lightly with a fingertip.
Loosen the cake around the edges with a knife; invert the pan onto a clean tea towel.
Peel off the wax paper.
Starting at the short end, roll up the cake and towel together.
Place the roll, seam-side down, on a wire rack; cool completely.