Defrost puff pastry slices side by side at room temperature. Peel and finely dice the shallots. Heat butter in a small pan. Sauté shallots for 3-4 minutes. Add vinegar and sugar and caramelise for about 10 minutes.
Heat the oil in a pan. Halve the white sausages lengthwise and fry them in the pan for approx. 5 minutes while turning. Remove the sausage from the pan and let it cool down.
Season the shallots with salt and pepper, remove from the heat and allow to cool slightly. Lay the puff pastry slices on top of each other and roll out rectangularly (approx. 22 x 44 cm) on a floured work surface.
Cut the dough into 8 squares. Spread each square of dough with caramelized shallots, leaving about 0.5 cm of edge free. Put 1/2 white sausage on each square and roll up in the dough.
Slightly scratch the surface. Place the dough rolls on a baking tray lined with baking paper. Whisk the egg yolk and milk, spread on the puff pastry. Place the rolls in a preheated oven (electric cooker: 225 °C/ convection oven: 200 °C/ gas: see
manufacturer) bake for about 15 minutes until golden brown. Remove and serve hot or lukewarm.