Start with the pastry. Place flour and chilled butter in a food processor. Process until the mixture looks like breadcrumbs. Add egg yolk and a little chilled water. Process again until the dough comes together. Turn the dough onto a lightly floured surface and knead it gently, then shape it into a disc. Wrap it up and pop it in the fridge for 30 minutes.
For the roasted veggies, preheat the oven to 200 degrees Celsius. Wrap each beetroot in foil and place on a baking tray. Line another tray with baking paper and add carrots, pumpkin and tomatoes. Spray with oil and season with salt and pepper. Roast the beetroot for 10 minutes, then add the tomato mixture to the oven, and keep roasting for another 20 minutes, or until the vegetables are tender. Roll out the pastry on a lightly floured surface, until about 3 millimetres thick. Line your tart tin with pastry and trim the excess. Then chill it for another 15 minutes.
In the meantime, heat a frying pan over medium heat and spray with oil. Cook the leek for 3-4 minutes, turning occasionally, until it's just tender. Set it aside to cool slightly. To blind-bake the tart case, line it with baking paper and fill it with pastry weights or rice. Bake on a baking tray for 10 minutes. Now remove the paper and the weights or rice and bake for another 10 minutes, until the pastry is light golden. Reduce the oven temperature to 160 degrees.
Put eggs in a bowl with cream and cheddar and whisk together. Season with salt and pepper. Wear gloves to peel the beetroot to avoid staining your hands. Cut in half. Arrange over the base of the tart case with the pumpkin, carrot, leek and zucchini. Pour the egg mixture around the vegetables in the tart case. Sprinkle with goat's cheese.
Bake for 30-35 minutes, or until the filling is just set. Leave the tart to cool in the tin for about 5 minutes, then carefully transfer it to a serving platter. Top with roasted tomatoes and thyme sprigs. Serve warm or at room temperature.