As soon as the cake is cool enough to touch, pick up the edges of the parchment paper and pull the cake out of the pan. Gently the cake face-down on the sugar-covered dish towel.
Gently peel the parchment paper off the cake.
While the cake is still warm, roll the dish towel up tightly with the cake inside. This will prevent cracking and tearing when you roll the cake later.
Gently unroll the dish towel and the cake, and allow the cake to sit and cool for at least 30 minutes.
Make the raspberry jam:
The jam can be made up to 3 days ahead of time and stored in an airtight container in the fridge. Or, you can make the jam while you're waiting for the cake to cool.
Combine the raspberries, sugar and water in a saucepan over medium-high heat. Cover the saucepan and bring to a boil.
Turn the heat down to medium-low and simmer for about 15 minutes with the lid on.
Remove the lid and simmer for another 15 minutes, until most of the liquid evaporates and the raspberries reach a jam-like consistency.
Remove from the heat and stir in the vanilla extract