- Preheat the oven to 350°F (180°C) and grease a 12-inch (30 cm) tart dish with butter. Set aside.
- Melt the butter in a large sauté pan placed over medium-high heat. Once melted, add the shallots, and gently stir-fry for about 5 minutes, turning from time to time until just beginning to brown.
- Add the sugar, balsamic vinegar, and cook for a further 5 minutes, moving and shaking the pan occasionally so the shallots do not stick to the pan. Season with salt and pepper.
- Arrange the halved parsnips and carrots to the bottom of the tart dish, face down, so they make a pretty pattern when you will later invert the tart. Add the caramelized shallots in the remaining holes, then pour the balsamic reduction over the vegetables.
- Add feta cheese on top and sprinkle fresh thyme all over.
- Lift the crust over the filling and tuck down the sides of the dish. Make two small slits for the steam to escape.
- Bake for about 30 minutes until the pastry is well risen. Leave to stand for five minutes. Cover the dish with a plate, invert, then remove the dish, leaving the tart now on the plate. Sprinkle additional black pepper and serve warm, with a side of lettuce.
* For homemade pie crust you will need 3.5 ounces (100g) diced unsalted butter, 1 ⅔ cups (200g) all-purpose flour, 1 pinch of salt, 5 Tablespoons cold water. Mix all the ingredients until they stick together and form a ball. Roll out the dough into a large disk, leaving a border a little larger than the tart dish.