For the crust: Pulse the flour, salt and baking powder in a food processor until combined. Add the butter, one piece at a time, pulsing until the mixture looks like coarse meal. Pulse in the parsley. Separate the egg; refrigerate the egg white. Beat the egg yolk and milk in a small bowl, then add to the food processor, pulsing until the dough starts to clump together. Turn the dough out onto a lightly floured surface, and gather into a ball. Flatten into a disk, wrap in plastic wrap and chill at least 1 hour.
For the filling: Meanwhile, cook the pancetta in the oil in a large skillet over medium heat, stirring, until browned and crispy, 10 to 12 minutes. Remove the pancetta to a paper towel-lined plate with a slotted spoon; reserve. Increase the heat to medium-high, and add the onions to the pancetta drippings, spreading them into a single layer. Leave them untouched until the bottoms have browned, 2 to 3 minutes. Add the vinegar, and scrape the bottom of the pan. Stir in the thyme, red pepper flakes, salt and a few grinds of black pepper. Add the flour, stir until the onions are coated, then whisk in the heavy cream and chicken broth. Bring to a simmer, and cook until the onions are soft and the sauce is reduced to the consistency of melted ice cream, 18 to 20 minutes. If the onions are still not quite tender and the sauce is too thick, add a few tablespoons of water at a time to loosen the sauce while the onions soften. Cool for 5 minutes so the pie is less steamy when you put the top crust on.
Preheat the oven to 425 degrees F. Pour the filling into a 9-inch pie dish. Scatter the pancetta over the filling. Roll out the dough on a lightly floured surface to about 1/4 inch thick and 10 inches in diameter. Cover the pie with the dough, and press it onto the sides of the dish. Crimp the edges with your fingers, or press with a fork. Beat the reserved egg white in a bowl, and brush it over the dough. Cut vents in the top of the pie, and place it on a rimmed baking sheet to catch any drips. Bake until the crust is browned, about 25 minutes. Let cool for 10 minutes on a baking rack.
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