Preheat oven to 375 °F. Line rimmed baking pan , 15 1/2 x 10 1/2 x 1 inch, with waxed paper and grease generously.
In a small bowl, sift together flour, cocoa, baking powder, and salt. Set aside.
To the large bowl of a stand mixer, add eggs. Beat at high speed until thick and lemon colored, about 5 minutes. Gradually beat in granulated sugar. On low speed, beat in water and vanilla. Gradually add flour mixture; beating just until smooth. Evenly distribute batter in prepared pan. Bake until wooden toothpick inserted in center comes out clean, 12 to 15 minutes.
Meanwhile, place paper towels that are slightly wider and longer than cake pan on a clean work surface and sprinkle generously with confectioner's sugar. When cake is done, immediately loosen from edges of pan, and invert on prepared paper towels. Carefully remove waxed-paper. Trim off edges, if necessary. While hot, carefully roll up cake together with towel from narrow end. Cool on wire rack at least 30 minutes.