Preheat the oven to 180°C and place a pizza stone or heavy tile on the centre shelf. Roll out the pastry to a 32cm disc, then line into a 26cm tart tin. Trim the edges and chill until firm.
Meanwhile, combine 100g butter with the sugar and vanilla in the bowl of an electric mixer and beat with the paddle attachment on medium speed for 5 minutes until light. Add the eggs and beat well. Fold in the almond meal. Spread into the bottom of the tart shell, then chill again.
Melt the remaining butter with the brown sugar and lemon juice. Halve and core the apples, then slice very finely on a mandolin and toss thoroughly in the lemon mixture. Set aside for 20 minutes to soften. Arrange 12 apple slices in an overlapping row, then roll up tightly and arrange upright on the almond mixture. Repeat with the remaining apples until the tart is covered.
Place the tart on the preheated pizza stone and bake for 30 minutes until the pastry is well browned. Dust thoroughly with icing sugar and bake again for 5 minutes until the peaks begin to darken. Serve with ice cream and berries.
*Homemade or store-bought