Preheat the oven to 180°C. Add the onions and extra virgin olive oil to a medium-low heat pan and sweat down for 15 minutes until they start to soften. Add the thyme leaves, sea salt and caster sugar & continue to stir regularly until they are golden & caramelised. The process should take about 40 minutes.
Add the crème fraîche & the balsamic vinegar to the onions and combine.
Add the puff pastry sheet to an oven proof tray lined with baking paper. With a knife, gently draw a rectangle around the edges to create a border & then with a fork gently prick evenly across the pastry.
Add the onions to the area that you pricked with a fork and spread them out in an even layer.
Add a generous grating of Parmigiano Reggiano DOP and bake in the oven for 20-25 minutes until the pastry is golden.
