Preheat the oven to 375°F. Meanwhile, in a large skillet over medium-high heat, add the oil, onion, and potato, and season with salt to taste. Cook, stirring, until warmed and sizzling, about 3 minutes. Add the beef, 1½ teaspoons salt, and a generous pinch of black pepper. Cook, breaking up the beef with a wooden spoon or spatula, until the beef is no longer pink and some of the liquid has evaporated, about 15 minutes. Stir in the vinegar and garlic, and continue cooking until the vinegar has mostly evaporated, about 2 minutes more.
Turn off the heat and stir in the cheese, broccoli rabe, and a generous pinch of chile flakes until evenly distributed. Taste and adjust the seasoning with more salt, pepper, and chile flakes as needed. Transfer to a large, wide bowl and let cool completely.
When the mixture is cooled, retrieve the puff pastry from the refrigerator. On a lightly floured surface, roll out 1 sheet of pastry to about ⅛-inch thickness and trim into a 12-inch round. Transfer to a 10-inch cast-iron skillet or deep-dish pie plate. Roll the remaining sheet to about ⅛-inch thickness and trim into a 12-inch round. Using a slotted spoon, transfer the beef mixture to the pastry-lined skillet. Lightly brush the edges with some of the egg mixture, then place the remaining round of pastry on top. Press the edges to seal, trim all but ½ inch of overhang, and crimp.
Transfer the pie to a foil-lined baking sheet. Lightly brush the top with more of the egg mixture (you will have some left over). Using a sharp paring knife, cut an "X" in the center for ventilation. Lightly sprinkle with salt and black pepper.
Bake until the top crust is golden brown and puffed, and the bottom crust is set and easily pulls away from the sides of the skillet, 45–50 minutes (if the crust is browning too quickly, gently tent with foil). Transfer the skillet to a rack and let cool for 10–20 minutes, then slice the pie into wedges and serve.