To start, prepare the crust. In a food processor, pulse together all-purpose flour, pine nuts, and salt until everything is finely ground and well-combined. This step is crucial for achieving a smooth and flavorful crust.
Next, add the cold unsalted butter cut into cubes. Pulse the mixture until it resembles pea-sized crumbles. You want to achieve a texture that will create a flaky crust once baked.
Now, add the large egg and the reserved egg yolk. Pulse again 3 to 4 times until the mixture is evenly moistened. If it still feels too dry, you can add a tablespoon of cold water, ensuring the crumbs stick together when pinched.
Transfer the crumb mixture onto a piece of plastic wrap. Knead it a couple of times to form a ball, then flatten it into a disc. Wrap it tightly in plastic wrap and refrigerate for at least 30 minutes. This chilling step is essential for helping the crust maintain its shape while baking.
While the crust is chilling, preheat your oven to 400 degrees F. Meanwhile, prepare the golden beet. Trim the stem end, rub it all over with olive oil, and wrap it loosely in aluminum foil.
Roast the wrapped beet in the oven for 40 to 45 minutes until it's fork-tender. Once it's done, remove it from the oven and let it cool for about 10 minutes. After cooling, rub the beet between two paper towels to remove the skin, which should come off easily.
Once the beet is peeled, slice it and cut it into ¼-inch dice. Set aside. Now, reduce the oven temperature to 375 degrees F.
On a lightly floured surface, roll the chilled crust dough into a 7-by-11-inch rectangle, about ¼-inch thick. Using a cookie cutter or a small bowl, cut out 3 ½-inch rounds. Carefully ease these rounds into mini pie cavities, being cautious not to stretch the dough.
To prevent shrinkage during baking, place mini muffin papers inside each crust, filling them with pie weights or dried beans. Bake the crusts for 10 minutes, then remove the weights and papers, brushing the insides with the reserved beaten egg white. Bake for an additional 5 minutes or until the edges are just barely golden.
Remove the crusts from the oven and let them cool for at least 10 minutes. Meanwhile, prepare the filling. In a bowl, whisk together the egg, whole milk or half-and-half, thyme, rosemary, garlic, ground nutmeg, and a pinch of salt and black pepper. This filling will create a creamy and flavorful base.
Next, spoon 1 tablespoon of the diced golden beet into each crust. Then, pour the filling mixture into each crust, filling it within ¼-inch of the tops. You may end up with some leftover filling.
Sprinkle the tops with crumbled goat cheese and a few extra pine nuts for garnish if desired. This adds extra flavor and a beautiful finish.
Finally, bake the quiches for 15 to 18 minutes, or until the tops are set, no longer jiggly, and the edges of the crust are golden brown. Once done, let them cool slightly, then carefully remove them from the pan using removable bottoms. Serve them warm or at room temperature for the best experience.