Finely chop the onion and mushrooms.
Heat the oil in a pan over medium heat until hot. Add the onion, stir-fry for 3 minutes, then add the mushrooms. Stir for a minute then add the soy sauce. Let it bubble for a minute then stir in the rice wine vinegar mixed with the miso and deglaze the pan for a couple of minutes.
Transfer the mushroom mixture to a small bowl and let it cool, then chill if you want to bake the puffs later.
Preheat your oven to 190C.
Unroll the puff pastry, then cut it into small squares with a pizza cutter - 3 cuts horizontally and 4 vertically. So you should end up with 12 squares.
Using a blunt knife, draw a square about 1cm in from the edges, creating a border.
Spoon the mushroom mixture in the middle squares and spread it around, up to the line.
Put the squares onto a lined baking sheet, then scatter some sesame seeds on the top of each tartlets.
Bake in the middle of the oven for 10-12 minutes until golden, then transfer them to a plate to cool.
Serve warm or at room temperature.