Preheat the oven to 180°C, 350°F, Gas Mark 5.
Roll out the pastry onto a lightly floured surface. Scatter the pastry with the thyme leaves and Parmesan and, using the rolling pin, lightly press them into the pastry. Press the pastry into the bottom of a tart tin and bake blind for 10-15 minutes or until the pastry is pale gold and lightly cooked. Set aside.
Meanwhile heat the butter and olive oil in a pan and gently cook the onions with a little sugar until deep gold and sweet – 20-30 minutes. Spoon the onions onto the pastry base, then top with the sliced tomatoes. Sprinkle with a little sugar, salt and pepper.
Turn the oven up to 200°C, 400°F, Gas Mark 6 and return the tart to the oven for around 25 minutes or until the pastry is cooked and the tomatoes are softened. If the pastry starts to burn, cover with a rim of foil. Top with slices of goat's cheese and scatter with the hazelnuts, then pop back in the oven for five minutes or so to soften the cheese.