Prepare the shortbread: whisk the egg yolks and sugar until the mixture whitens. Add the two butters by mixing with a spatula, then the flour and baking powder by sifting. When the preparation is homogeneous, seal it in cling film and leave to stand for 1 hour in the refrigerator.
Turn on the oven at 180° (th. 7). Remove the dough from the cold and let it warm up for about 15 minutes before spreading it on a sheet of baking paper about 1.5 cm thick. Slide the sheet on the baking sheet and cut with circles of discs 5 to 6 cm in diameter. Remove the dough between the discs and slide the baking sheet into the oven, leaving the metal circles around the dough. Bake for 25 to 30 min, until the shortbread is blond. Remove from the oven and leave the shortbread to cool.
Prepare the fruit: peel the mangoes and cut them into thin wedges; peel the pineapple and cut into vertical slices 1.5 cm thick and then into small rectangles.
Heat the hazelnut oil and butter in a non-stick frying pan over low heat. Quickly brown the fruit and set aside on a plate. Pour the sugar and mango balsamic into the pan and allow to caramelize. Return the fruit and its juice to the pan, stir to coat the fruit with a thick, fragrant juice.
Divide the shortbread into 8 plates, garnish with fruit and top with juice. Rinse the lemon, pat it dry and grate the zest over the plates. Serve immediately, the fruit still warm.