Heat 2 tablespoons of the olive oil in a frying pan on a medium heat. Add the shallots along with the chilli flakes, thyme (reserving a few leaves for garnish), vinegar, and seasoning. Cook for 20 – 25 minutes until dark brown, caramelised and sticky.
Slice the bottom third from each peach and then carefully remove the stone.
Preheat the oven to 180°C. Roll out the puff pastry onto a baking tray, leaving it on its greaseproof paper. Using a small bowl as a guide, cut the puff pastry into circles large enough to contain the peaches. Save the discards for another recipe.
Cut a 2cm border around the edge of each tart. Fill the centre of each tart with a tablespoon of the caramelised shallot mixture. Top each tart with the larger portion of the destoned peach. Drizzle with a little more extra virgin olive oil and a sprinkling of sea salt and black pepper.
Whisk the egg in a small bowl, then use a pastry brush to paint the border of each tart with it. Place into the oven to cook for 20 minutes until the peaches are soft and the pastry is golden and puffed up.
Finish the tarts with a drizzle of honey, a slice of Prosciutto, a generous grating of Parmesan and a few thyme leaves.