Frenching, or French cutting, onions, refers to thinly slicing onions into strips. I learned this method from my friend Suzanne, who has contributed several recipes on this site. There may be a more precise term for this method, but neither one of us knows it (if you do, please let us know).
3 Standing the onion up, root-side up, cut the onion in half. Then take each half and make thin slices. Slice the onion in a way that keeps the onion segments attached to the root end, as shown in the photograph.
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.
2 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.
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.
1 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.
2 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.