Preheat your oven to 180C / 350 F. Spread the beets and onions on two separate trays, ensuring they have enough space to roast evenly. Drizzle olive oil over each tray, using about a tablespoon for each, and toss the vegetables to coat them well. Place them in the preheated oven.
Roast the onions for about 40 minutes and the beets for an hour, until they are tender and caramelized. The onions should become golden and sweet, while the beets will develop a rich and earthy flavor.
While the vegetables are roasting, prepare the pastry. In a food processor, combine the cake flour, whole-wheat flour, and a pinch of salt. Pulse briefly to mix. Add the butter cubes and pulse until the mixture resembles breadcrumbs, which should take about 10 seconds.
Gradually add the ice-cold water while pulsing until the dough just comes together. Be careful not to overmix; you want a crumbly texture that holds together when pressed. Wrap the dough in cling film and refrigerate it for at least 30 minutes to chill.
After the vegetables are roasted and the dough has chilled, roll the pastry out on a floured surface into a rustic round shape. Aim for about a 12-inch diameter. It doesn’t have to be perfect; the rustic look adds to the charm of the galette!
In a small saucepan, combine the brown sugar and balsamic vinegar. Heat it over medium heat and allow it to bubble for about 5 minutes, stirring occasionally until it thickens into a syrupy consistency. This sweetened balsamic will enhance the flavors of the vegetables.
Once the beets and onions are roasted, toss them together in a bowl and place them in the center of the rolled-out pastry. Leave enough edge around the outer rim for folding.
Drizzle the balsamic syrup over the vegetable mixture and season generously with sea salt and freshly ground black pepper.
Fold the edges of the pastry over the filling to create a rustic border, pinching it together to secure. Brush the exposed pastry with melted butter or a beaten egg for a beautiful golden finish.
Bake the galette in the oven for 25 to 30 minutes or until the pastry is golden brown and crisp. The aroma will fill your kitchen, hinting at the deliciousness to come.
Once baked, remove the galette from the oven and allow it to cool slightly. Shave the goat cheese over the top and serve warm or at room temperature.
