Lightly dust a workbench with flour and roll out the puff pastry to a thickness of 5mm. Cut out 4 square cases 8cm × 8cm from the pastry. Place the pastry cases on a cold baking sheet and prick with a fork. Rest the pastry in the fridge for 30 minutes.
Place a square pastry cutter 4cm × 4cm in the centre of the 4 pastry cases and spoon a thin layer of Lyonnaise onion into it. Using the back of the spoon to smooth it evenly over the pastry. Remove the pastry cutter and brush the border of the pastry with egg wash. Refrigerate the pastry cases to rest for another 30 minutes.
Pre-heat the oven to 200°C. Lightly spray another baking tray with water and transfer the Lyonnaise tarts onto it. Bake in the oven for 8 minutes or until the pastry is crisp and golden. While the tarts are baking, finish cooking the sweetbreads.
Warm the sauce Soubise over a gentle heat. Heat the vegetable oil in a heavy-based cast-iron pan. Lightly season the sweetbreads with salt and freshly ground pepper, place in the pan and fry for 2 - 3 minutes until browned. Turn, and cook the other side. Add the whole butter, garlic and thyme to the pan and baste the sweetbreads with the butter for a further 2 minutes. The outside of the sweetbreads should be browned and crisp while the inside should remain moist and creamy. Remove the sweetbreads from the pan and keep warm.
Spoon 20ml sauce Soubise into the centre of a warm plate and spread with the base of the spoon to form a neat circle. Place a Lyonnaise tart in the centre of the sauce Soubise. Top the sweetbreads with 4 slices of truffle and place in the centre of the Lyonnaise tart. Spoon the red wine jus over the sweetbreads and around the sauce Soubise.