With the rack in the middle position, preheat the oven to 180 °C (350 °F). Line a 38 x 25-cm (15 x 10-inch) baking sheet with parchment paper and butter.
In a bowl, beat the eggs with an electric mixer until foamy. Add the sugar and vanilla extract. Beat until the mixture thickens, about 5 minutes.
In a bowl, sift together the flour and baking powder. With a spatula, fold into the egg mixture. Stir in the butter. Spread on the baking sheet.
Bake for about 15 minutes or until a toothpick inserted in the centre of the cake comes out clean. Right out of the oven, flip the cake onto a sheet of parchment paper sprinkled with granulated sugar. Roll the cake and let cool. Unroll and spread with the chosen filling.