Step 1Place the butter, egg, sugar, milk and salt in the bowl of a food processor. Pulse on/off until the butter is coarsely chopped. Spoon the flour evenly over the butter. Process just until the dough is crumbly and beginning to cohere but not in a ball (overprocessing will toughen the dough). Transfer the dough to a work surface. Gather the dough together and knead it, folding it back on itself, until it's in a smooth ball. Flatten it into a disk. Wrap the dough in plastic; refrigerate at least 2 hours or up to 2 days. (It can also be frozen up to 1 month; thaw in the refrigerator.)
Step 2Let the chilled dough rest at room temperature for 10 minutes before rolling. Roll the dough on a well-floured surface into a circle about 1/4 inch thick. Do not roll it too thin; it tastes better thicker. Transfer it to a 9-inch quiche or springform pan (1 to 1 1/2 inches deep) with a removable bottom. Press it into place without stretching the dough. Trim the pastry edge for a 1-inch overhang. (Reserve any pastry scraps for patching later.) Fold the overhang inside to form double-thick sides. Press this dough firmly into place, pushing the crust up 1/4 inch above the edge of the pan to allow for any shrinkage during baking. Refrigerate until the dough is firm, about 1 hour (or freeze briefly). Line the shell with parchment paper or foil; fill with dried beans.
Step 3Heat the oven to 375 degrees.
Step 4Bake until the dough is starting to set, about 16 to 18 minutes. Carefully lift out the paper and beans; continue to bake until lightly browned, about 15 minutes more. Patch any cracks with thin scraps of the reserved dough; it is not necessary to bake patches. The shell can be filled while still hot from the oven.
Step 1Place the bacon and 1/2 cup of water in a nonstick skillet. Bring to boil, then drain off the water. Cook the bacon over medium-high heat until browned, stirring often, about 4 minutes. Set aside.
Step 2In the same pan, combine the oil, water, onions, salt and pepper to taste; cook over medium-high heat, covered, stirring occasionally, for 4 minutes. Uncover, add the sugar and cook until lightly browned, about 4 more minutes. Stir in the flour. Remove from the heat. Stir in the cream, milk, eggs and reserved bacon.
Step 3Carefully ladle the filling into the baked crust; use a fork to evenly distribute the onions and bacon. Sprinkle evenly with the cheese, then the chives (or if making ahead, sprinkle with chives when reheating to keep their bright color).
Step 4Place the quiche on a baking sheet and bake at 375 degrees until browned and puffy, about 35 to 40 minutes.Cool on a rack at least 10 minutes before serving. (The quiche can be cooled completely and refrigerated overnight. Before reheating, let it come to room temperature. Reheat at 300 degrees for 15 minutes.)
Step 5To serve, transfer the quiche from pan to platter. Serve warm or at room temperature, cut into wedges.