Preheat oven to 375°F (190°C). Line a 15x10-inch jelly roll pan with parchment paper, slightly greasing the paper.

In a large bowl, beat the egg yolks and granulated sugar until pale and thick. Gently fold in the sifted flour, baking powder, salt, and vanilla extract until just combined. Do not overmix.

In a separate clean bowl, beat the egg whites until stiff, glossy peaks form. Gently fold one-third of the egg whites into the yolk mixture to lighten it, then fold in the remaining egg whites until no streaks remain.

Spread the batter evenly into the prepared pan. Bake for 12-15 minutes, or until the top springs back lightly when touched. While hot, invert the cake onto a clean kitchen towel dusted generously with powdered sugar. Carefully peel off the parchment paper. Roll the cake up tightly along with the towel and allow it to cool completely on a wire rack.

While the cake cools, prepare the filling: Beat the softened butter until creamy. Gradually add powdered sugar, vanilla, and milk until the buttercream is light and fluffy. Set aside.

Prepare the chocolate ganache: Heat heavy cream until simmering. Remove from heat and pour over the chopped chocolate. Let sit for 5 minutes, then gently whisk until smooth. Let cool slightly until spreadable.

Unroll the cooled sponge cake carefully. Spread the vanilla buttercream evenly over the entire surface. Re-roll the cake tightly without the towel. Chill for at least 30 minutes to set.

Decorate the chilled Swiss roll by drizzling or swirling the softened chocolate ganache across the top for a festive birthday look. Slice and serve cold.