Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a mixing bowl, whisk together the flour, baking powder, and salt.
In another bowl, beat the eggs and sugar until pale and fluffy, about 5 minutes.
Mix in the melted butter and vanilla extract until smooth.
Gently fold the dry ingredients into the wet mixture until just combined.
Pour the batter onto the prepared baking sheet, spreading evenly.
Bake for 12-15 minutes until the cake springs back when lightly pressed.
Remove from the oven and let it cool in the pan for 5 minutes before transferring to a wire rack.
Once cooled, spread the raspberry puree evenly over the cake.
Starting from one end, gently roll the cake into a log shape, using parchment to assist if necessary.
Wrap the rolled cake in plastic wrap and refrigerate for at least 1 hour to set.
Prepare the icing by combining powdered sugar and a few tablespoons of raspberry puree until smooth.
Unroll the chilled cake, drizzle the icing over the top, and re-roll it carefully.
Garnish with fresh raspberries before serving.