Put the baking sheets in the oven and heat to 200C, fan 180C. Heat the oil in a large pan, then soften the onion for 5 minutes. Turn up the heat, then add the 1 tbsp each of balsamic vinegar and brown sugar. Bring to the boil, then simmer for 5 minutes until tender and sticky. Leave to cool a little, then season to taste.
Roll out the pastry and cut into four equal sized rectangles. Lift onto the hot baking sheet, prick the pastry a few times with a fork, then place three red onion segments on to each, leaving a 1.5cm border along the edge. Crumble a few pieces of goats cheeses, then top with a rosemary sprig. Brush the edges of the pastry with the egg, then chill until ready to bake.
Bake for 20 minutes or until golden and crisp.
Meanwhile, make the strawberry compote. Add the strawberries, remaining balsamic vinegar and brown sugar into a small pan, and bring to a simmer for a few minutes, or until the strawberries begin to break down a little. Add the red wine and simmer for a further five minutes. Remove from the heat and set aside until needed.
Serve the tarts with a little rocket salad and a spoonful of strawberry compote.