Heat onions, sugar, balsamic vinegar, and water in a saucepan and cook until reduced by half, stirring occasionally.
Cut the third red onion and the potatoes into thin strips. Brush the potato slices with olive oil and cut the cheese into slices.
Roll out the puff pastry dough and cut it vertically into six equal strips. Spread the onion chutney onto each strip and cover with a slice of bacon. Arrange the potato slices so that they overlap the edge of the dough. Season with salt and pepper, then add the onion slices so that they are also peeking over the dough's edge.
Line the bottom edge of the dough lengthwise with the cheese slices, then fold over and roll the strips up, creating a flower effect.
Place the potato flowers in the indentations of a muffin tray and bake at 350 °F for 25 minutes.