In large mixing bowl beat the eggs with whisk attachment until thick and pale in color.
Add in the sugar and vanilla, mix until well combined and mixture leaves a trail in the bowl.
In a medium bowl, sift the flour, cocoa, salt, and baking powder. Fold dry ingredients into the batter. Batter will start out streaky, continue folding until mixture is completely combined.
Mix the melted butter and milk in a bowl.
With mixer on low, slowly add the butter and milk mixture to the cake batter. Mix until just combined.
Pour batter (batter is pourable) into prepared pan and spread with spatula so batter is evenly spread corner to corner.
Bake until center of the cake springs back when gently pushed on - about 10 - 12 minutes.
Let cake cool for 5 minutes. Loosen the edges of the cake by gently lifting up on the parchment at the corners.
Using the parchment under the cake, start rolling the cake up. Roll up from the long side, not the short side. This will give enough length to cut a side branch and top branch.
Place rolled up cake, seam side down, onto a cooling rack and cool completely, about 60-90 minutes. (Do NOT cool overnight or cake will be too stiff and will break when you try to unroll it.)