Preheat the oven to 180ºC/gas 4 and line a 28cm x 35cm Swiss roll tin with greased greaseproof paper.
Melt the butter in a saucepan over a medium-low heat, until it starts to turn golden brown and smells deliciously nutty.
Remove from the heat and leave it to cool at room temperature.
Crack the eggs into the bowl of a free-standing mixer, add the caster sugar and vanilla and whisk it on a medium-high speed for 3 to 4 minutes, or until tripled in volume, thick and pale, and leaves a trail when the whisk is lifted from the bowl.
In a bowl, stir together the flour, ground almonds and baking powder with a pinch of sea salt, then gently fold this into the egg mixture.
Pour the cooled butter around the inside edge of the bowl and gently fold this in too.
Spoon the batter into the prepared tin, spread it level and scatter over the flaked almonds.
Bake it on the middle shelf of the oven for 10 to 12 minutes, or until the cake is golden, risen and springy.
Leave the cake to cool in the tin for a couple of minutes before transferring it, still on the paper, to a wire cooling rack to cool completely.
Use a 6cm cookie cutter to stamp out circles from the cake and place them top-side down on your work surface (if the cake is quite thick, halve it horizontally). Spread the underside of each with jam.
Using the same cutter, stamp out discs from the ice cream slab, then sandwich each with jammy sponge, and serve.