Preheat your oven to 180°C (350°F). Line the baking sheet with parchment paper, ensuring it extends slightly over the edges for easy removal later.
In a large mixing bowl, beat the eggs and granulated sugar using an electric mixer until the mixture is thick and pale, about 5-7 minutes. Add 1 teaspoon vanilla extract and mix well.
Sift together the flour, baking powder, and salt in a medium mixing bowl. Gradually fold the dry ingredients into the egg mixture using a spatula. Be careful not to deflate the batter.
Gently fold in the melted butter until just combined. Pour the batter onto the prepared baking sheet, spreading it evenly with an offset spatula.
Bake in the preheated oven for 12-15 minutes, or until the cake is lightly golden and springs back when touched. Remove from the oven and let it cool for a few minutes.
While the cake is still warm, invert it onto a clean kitchen towel dusted with powdered sugar. Carefully peel off the parchment paper.
Starting from one end, gently roll the cake up with the towel inside, creating a spiral. Allow the rolled cake to cool completely.
Meanwhile, whip the heavy cream with 2 tablespoons powdered sugar and 1 teaspoon vanilla extract until soft peaks form. If desired, add food coloring to achieve your preferred pastel shades.
Unroll the cooled cake carefully. Spread the whipped cream evenly over the surface and arrange the mixed berries on top.
Roll the cake back up without the towel and wrap it tightly in plastic wrap. Refrigerate for at least 30 minutes to set.
Once set, slice the Swiss roll into portions and serve on a platter, garnished with extra berries if desired.