Slicing Onions Stem to Root To caramelize onions, you'll want to slice them lengthwise, or from stem end to root end. That way the onions will hold their shape better during the long cooking involved in caramelizing.
First, use a sharp knife, get a firm grip on the onion, and slice off the stem end of the onion, by about a 1/2 inch. Then place the onion cut side down on the board to stabilize it, and cut it in half, straight through the root end.
Peel back the papery skin of the onions. If you want, to keep your cutting area clean, cut off the roots with the skins, but cut only enough to cut off the messy roots. Keep the root end intact. It will make it easier to slice the onion.
With an onion half cut-side down on the board to stabilize it, make angled cuts into the onion, from stem end to root end, cutting to, but not through the root end. Work your way around the arc of the onion, aiming your knife's blade toward the center of the onion.
Make a "V" cut in the root end of the onion to cut out the tough root end, to release the onion slices.
Pre-Baking the Crust 1 On a lightly floured surface, roll dough into a 12-inch circle. Fit into a 9-by-1 1/2-inch round tart pan, pressing dough into corners. Transfer to freezer to chill for 30 minutes.
Preheat oven to 350°. Line pastry with parchment paper, wax paper, or aluminum foil, pressing into the corners and edges. Fill at least two-thirds with baking weights - dried beans, rice, or aluminum pie weights. Bake first for 15 minutes, remove from oven and let cool a few minutes. Carefully remove parchment paper and weights. Poke the bottom of the pie pan with the tines of a fork and return to oven and bake an additional 10 minutes or until lightly golden. (Fork holes are for any air to escape.) Transfer to a wire rack to cool while making filling.
Caramelizing the Onions and Preparing the Quiche The onions will take about an hour to cook on the stovetop before they are ready to go into the quiche. So timing-wise, if you are making the entire quiche from scratch, it makes sense to get started on the onions once you've put the crust into the freezer to chill before pre-baking.
Heat olive oil in a large, heavy-bottomed sauté pan on medium heat. Add the onions and sprinkle a little salt over them. Cook, stirring occasionally for 10 minutes, until the onions have softened and are translucent. Reduce the heat to medium low and cook for an additional 40 minutes, stirring occasionally, until the onions are well browned. Add balsamic vinegar and cook for 10 minutes more, until onions are completely caramelized. Remove from heat.
Place tart pan on a baking sheet to catch any run-off there might be. Sprinkle half the cheese evenly over the bottom of the crust. Spread onions over the cheese and then top with remaining cheese. In a medium bowl, whisk together milk, cream, and eggs. Season with nutmeg, salt, and pepper. Pour over cheese. Transfer to oven, and bake until just set in the center, 30 to 35 minutes. Cool on a wire rack for about 10-15 minutes before slicing.