Use a serrated palette knife to split the cake in half horizontally, so that you have two, thin layers.
Dice about 1/3 of the strawberries to go in between the cake layers, then thickly slice the remaining berries for the top of the cake.
Place the double cream and icing sugar into a large bowl and whisk until the cream is holding its shape, but still soft, smooth and billowy.
Take the chilled pastry cream out of the fridge and stir to smooth it out.
Place one of the cake layers onto a serving plate. Top with the pastry cream (reserving a small spoonful for later), spreading it out across the surface of the cake but leaving a small border around the edge, so that it doesn't ooze out later.
Add the diced strawberries over the top of the pastry cream, then dot the reserved pastry cream across the surface of the berries, to help the next cake layer stick.
Place the remaining cake layer on top, making sure it is level and lined up with the cake layer below. If the cake feels a bit unsteady, you can chill it at this stage for 5-10 minutes to help it firm up.
Cover the top and sides of the cake with a thick layer of whipped cream, then pile the sliced strawberries up in the middle of the cake. Just before serving, dust with icing sugar, if desired.
This jordgubbstårta is best served immediately. Leftovers can be stored in the fridge for a day or two (provided the cream/strawberries remain in date), but the cake will quickly start to dry out/toughen up. You can make the cake itself a day or so ahead of time, storing it in an airtight container before splitting, filling and decorating.