Cut the peppers in half lengthwise, clean and wash them. Brush the baking tray with oil. Place the bell peppers on top with the cut surfaces facing down. Brush the bell peppers with olive oil. In a preheated oven (electric cooker: 225 °C/ circulating air: 200 °C/ gas: see
manufacturer) bake for about 20 minutes. Remove from the oven, place on a cake rack and let cool.
Place the puff pastry slices next to each other on the work surface and let them thaw for 12-15 minutes. Wash the rosemary, shake dry and pluck the needles from the twigs.
Put the sugar, vinegar and butter in a tarte tatin pan (28 cm Ø at the top, 23 cm Ø at the bottom) and caramelise over a low heat until golden. Spread the rosemary in the pan, except for a little to garnish, and remove from the heat.
Distribute the peppers evenly with the skin side facing upwards.
Place the puff pastry sheets on top of each other and roll out into a square (approx. 25 x 25 cm) on a floured work surface. Place directly on top of the peppers, carefully fold the protruding edge inwards.
Bake in the preheated oven (electric cooker: 225 °C/ convection oven: 200 °C/ gas: see manufacturer) for approx. 25 minutes on the bottom shelf. Remove from the oven and immediately turn over onto a round board. Add some cream cheese in flakes.
Sprinkle with pepper and garnish with rosemary. Add the remaining cream cheese.