Butter and flour a 24cm loose-bottomed tart tin. Roll out pastry to 3mm thick. Cut out a circle allowing a 5cm border around the tin base. Gently ease pastry into the tin, carefully pushing in sides. Rest in refrigerator for 30 minutes.
Preheat oven to 180°C.
Lay plums in a roasting tray, cut side up. Place a piece of butter on top of each plum then sprinkle with the caster sugar.
Mix limoncello with 1 1/2 tbsp water and drizzle over plums. Roast for 20 minutes, basting occasionally, until softened but not collapsing. Remove from oven and set aside to cool.
Pour liquid from roasting plums into a small pan, then add the jam. Reduce over a low heat to create a glaze. Set aside.
Take pastry from fridge. Trim excess pastry and prick base a few times with a fork to prevent blistering and rising. Line tart tin with foil, add raw rice and blind-bake for 20-25 minutes. Remove from oven, lift out foil and rice, then return to oven and bake for 5-10 minutes, until the base has dried out.
For the filling, beat butter until light and creamy. Add sugar and mix until combined, then add ground hazelnuts and mix well. Add eggs, one at a time, mixing well after each addition. Gently fold in flour. Cover and refrigerate for 30 minutes.
Reduce oven to 160°C. Fill the tart case with filling (it should be about 2/3 full) then arrange plum halves on top, cut side up, so they are touching but not overlapping. Bake for about 40 minutes, or until a knife inserted into the middle comes out clean, then remove from oven.
Reheat plum glaze, then brush over tart. Scatter with the chopped toasted hazelnuts, slice and serve.