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1
Preheat oven to 400 degrees F.
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2
For crust, pulse flour together with pine nuts and salt in the bowl of your KitchenAid(R) Food Processor until finely ground and evenly incorporated. Add butter cubes and pulse until it forms pea-sized crumbles. Add egg and egg yolk (reserve remaining egg white for later) and pulse 3 to 4 more times until evenly moistened. If necessary, add up to 1 tablespoon of cold water until crumbs stick together when pinched between your fingers. Turn crumbs out onto a piece of plastic wrap, and knead once or twice until crumbs form a ball. Flatten slightly into a disc and wrap tightly in plastic wrap. Refrigerate for at least 30 minutes.
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3
Trim the stem end of the beet and rub all over with olive oil. Loosely wrap beet in aluminum foil, cut side down, gathering foil around the neck of the beet. Roast for 40 to 45 minutes until fork tender. Remove from oven at let cool about 10 minutes. When beet is cool enough to handle, rub between two paper towels; the skin should slide off easily. Slice and cut into a 1/4-inch dice.
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4
Reduce oven temperature to 375 degrees F. On a lightly floured surface, roll crust dough to a 7-by-11-inch rectangle, 1/4-inch thick. Cut out 3 1/2-inch rounds using a cookie cutter or trace the top of a small bowl with a pairing knife. Gently ease rounds into KitchenAid(R) Mini Pie Pan cavities, taking care not to stretch the dough. To prevent shrinkage, place a mini muffin papers inside each crust (or use a piece of parchment paper) and fill with pie weights or dried beans. Bake for 10 minutes, then remove weights and papers and brush with lightly beaten egg white. Bake for 5 minutes more or until just barely golden brown around the edges. Remove from oven and let cool for at least 10 minutes.
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5
For filling, whisk egg, milk or half-and-half, thyme, rosemary, garlic, nutmeg, and a pinch of salt and pepper.
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6
Spoon 1 tablespoon of diced beet into each crust. Pour in filling mixture to within 1/4-inch of the tops of the crusts. You may have leftover filling. Sprinkle with crumbled goat cheese and a few pine nuts on top, if desired.
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7
Bake quiches for 15 to 18 minutes or until tops are set and no longer jiggly, and edges of crust are golden brown. Let cool slightly, then remove from pan with the aid of removable bottoms. Serve warm or at room temperature.
