For the jam, place all the ingredients in a small saucepan and heat gently until the berries start to burst. Cook for a few minutes until the mixture thickens, then remove from the heat, strain through a sieve and set aside to cool completely.
For the pastry, rub the butter into the flour in a medium bowl until the mixture resembles fine breadcrumbs then stir in the sugar. Use a palette knife to cut in the beaten egg then press together to form a ball. Wrap in cling film and chill for at least 30 minutes.
Grease a 12-hole muffin tin. Unwrap the pastry, place a large sheet of greaseproof paper on top and roll out the pastry to a thickness of 3mm/⅛ in. Use a 5cm/2in round cutter to cut 12 bases for the mini tarts and place one in each hole of the muffin tin. Make the sides by cutting 12 strips 1cm/½in x 18cm/7in from the remaining pastry and gently press around the sides of each hole of the muffin tin. Chill for 15 minutes.
Preheat the oven to 170C/325F/Gas 3.
For the frangipane, place the ingredients in a bowl and beat with an electric mixer until smooth and thoroughly combined.
Prick the bases of the pastry cases then place half a teaspoon of the jam in each. Top with the frangipane mixture and bake in the oven for about 25 minutes until the frangipane is risen and golden. Cool in the tin for a few minutes then transfer to a wire rack.
For the topping, mix the icing sugar with a little water to form a thick paste. Spread over the cooled tarts and top each with one or two fresh blueberries.