Whip the cream with the vanilla in a chilled bowl until it begins to thicken. Add granulated sugar to taste, beating until the cream holds a good shape without being quite stiff—it will continue to stiffen as you spread it on the cake. Refrigerate the cream while you prepare the cake.

 Turn the cake best-looking side up on a platter. Cut it into two layers with a serrated bread knife. If the top layer is too delicate to pick up without breaking, slide a rimless baking sheet or a flexible plastic cutting mat under it and set it aside. Spread the bottom layer evenly with the preserves. Spread all of the whipped cream over the preserves. Set aside a few berries for garnish. Cut strawberries into bite-size pieces. Arrange berries or berry pieces over the cream in a single layer with a little space between them. Press the berries well into the cream (so the top cake layer will make contact with the cream). Set the top cake layer on top of the cream and press gently to level the cake. Cover and refrigerate for at least 2 hours, or up to 1 day.

Sieve a little powdered sugar over the top of the cake and garnish with the reserved berries and whipped cream, if desired, before serving. Leftovers keep in an airtight container in the refrigerator for a day or so.