Rub the butter and flour together in a large bowl using your fingertips. Work through the mixture until it resembles breadcrumbs. Stir in the sugar, egg yolk (reserve the white), vanilla extract and 2-3 tsp cold water to form a ball of dough that leaves the bowl clean. Wrap in cling film and chill for 30 mins.
Meanwhile, put the apple slices in a large bowl. squeeze over the lemon juice and cover with water. Microwave on High for 4 mins, then drain and pat dry on some kitchen paper. Heat oven to 190C/170C fan/gas 5.
Roll out the pastry to fit the tin and trim the edges with scissors so they stand up, about 5mm above the edge. Prick the surface of the pastry a few times with a fork. Place a layer of foil on top, add some baking beans and blind-bake for 15 mins. Remove the beans and foil, brush the pastry with the reserved egg white and return to the oven for 10-15 mins until biscuity.
Roll out 75g more of the marzipan out on a surface dusted with a little icing sugar until it’s approx 20 x 15cm. Cut into three rectangles and lay eight apple slices down the long edge of each strip of marzipan (see step-by-step guide) and reserve the rest. Fold the bare edge of each strip over to cover the apples, then roll up from the short edge (see step-by-step guide). Place the apple roses in eggcups or a muffin tin so that they hold their shape. Roll the remaining marzipan into small balls.
Mix the butter, sugar, eggs, almonds, flour and milk together in a large bowl and whisk until well combined. Take the tart case out of the oven and spread with the filling. Gently press your apple-marzipan roses into the filling, evenly spaced out, then scatter over the balls of marzipan. Fill the gaps with the remaining apple slices so that the filling is covered, curving the slices a little as you go to create additional petals on the roses, or rolling them up tightly to look like rosebuds, all with the peel-side facing upwards.
Return to the oven for 30-35 mins, then leave the tart to cool in the tin for 10 mins. Meanwhile, heat the apricot jam in a small saucepan until simmering, then pass it through a metal sieve into a bowl. Brush it over the surface of the tart while both the jam and the tart are still warm. Serve the tart a little warm, or leave to cool, then turn it out onto a serving plate and dust with icing sugar.