Heat double cream in a small saucepan until it starts to boil. Remove from heat and add the white chocolate, stirring well until the chocolate has melt completely.
Fill a bowl with cold water and ice. Transfer the ganache into a smaller bowl and place inside the first one to create an ice bath. With an electric beater, whip the ganache until it is silky and smooth. If still lumpy, refrigerate for a little while, then try beating again. Refrigerate the ganache while preparing the Swiss roll.
To make the hearts:
In a bowl, whip the egg white and sugar until stiff peaks form. Gently add the flour sifted with the cream of tartar (or baking powder). Mix in the red food colouring to desired colour is reached; spoon mixture into a piping bag.
Line a rectangular baking dish with baking parchment. Pipe out and fill some heart shapes; freeze the dish for 20 minutes.
For the Swiss roll:
Preheat the oven to 190 C / Gas 5.
Beat the egg whites and cream of tartar with an electric beater; add half of the sugar and continue to beat until stiff peaks form. In another bowl, using clean and dry beaters, beat the egg yolks with the remaining sugar until pale and very puffy.
Fold the egg whites into the egg yolk mixture with a gentle bottom-up movement. Add cooled melted butter and sift in the flour and cocoa. Mix gently as before.
Remove the tray of hearts from the freezer and pour the chocolate cake mixture on top of the hearts, spreading the mixture evenly.
Bake in the preheated oven for 7-8 minutes or until the top is dry but still soft. Remove from the oven and sprinkle a little sugar on top. Turn out onto a sheet of baking parchment that is slightly larger than the sponge. Peel off the lining paper. Trim the crusty edges of the sponge with a sharp knife and make a score mark 2.5 cm from one of the shorter edges (this will make the sponge easier to roll up). Carefully roll up the sponge from one of the short edges. Let cool completely at room temperature.
Unroll and spread with the white chocolate ganache. Spread the berries on the short side (that will go in the middle once rolled) and re-roll the cake.