Grease a 9-inch removable-bottom tart pan and place this on a baking tray.
For the Shortbread
Using a food processor, or mixer fitted with the paddle attachment, beat the butter, sugar, lemon juice, lemon rind, and brown sugar vigorously until pale and fluffy, about 3 minutes. It’s an important step to beat the butter and sugar well together when making shortbread as this ensures the shortbread is light, crisp, and will hold together.
In a separate bowl, sift the flour and salt. Add it to the butter mixture and mix until blended (forming large clumps).
Turn onto a floured surface and using floured hands, press two-thirds of the mixture evenly into the prepared pan (including the sides).
Spread with the blueberry preserves or jam evenly over the dough, leaving a ¼-inch border and then scatter with the blueberries.
Crumble the remaining dough into large crumbs and scatter evenly over the filling, covering most of the surface.
Bake the tart for 40 - 45 minutes, until lightly browned.
Leave to cool completely in the pan.
For the Lemon Icing
In a small bowl whisk together the powdered sugar, lemon juice, lemon rind, butter and one tablespoon of the milk. If it looks too thick, you can add a second tablespoon of milk.
Drizzle the cooled tart with the icing, remove from the pan and serve on the base.
NOTE: If your Blueberry Jam is quite sweet, you may want to skip the icing.