1. Prepare the Crust:

1. Preheat oven to 350°F (175°C). Line a 15×10-inch jelly roll pan with parchment paper and lightly grease.
2. In a large bowl, beat eggs on high speed for 5 minutes until thick and pale. Gradually beat in the 3/4 cup granulated sugar and vanilla. Gently fold in the flour, baking powder, and salt until just combined.
3. Spread the batter evenly into the prepared pan. Bake for 10-12 minutes or until the cake springs back when lightly touched.
4. Immediately turn the cake onto a kitchen towel dusted with powdered sugar. Carefully peel off the parchment paper. Starting with a short side, roll the cake and towel together into a log. Cool completely on a wire rack.
5. For the filling, beat the heavy cream and 1/4 cup powdered sugar until stiff peaks form. Unroll the cooled cake and spread an even layer of raspberry jam, followed by the sweetened whipped cream.
6. Re-roll the cake without the towel. Place seam-side down on a serving platter. Dust with more powdered sugar and garnish with fresh raspberries if desired. Chill for at least 1 hour before slicing.