1. Preheat the oven to 350°.
2. Set a large sauté pan over medium-high heat and add enough oil to just coat the bottom of the pan. When the oil is hot, add the beef and onions and cook until the meat is no longer pink, about 10 minutes. Drain off excess liquid. Add the stock, ketchup, Worcestershire sauce, oregano, nutmeg, ½ teaspoon kosher salt and ⅛ teaspoon pepper. Bring to a gentle boil, and cook for 5 minutes. In a small bowl, whisk together the flour and 1 tablespoon of water, then stir the flour mixture into the meat. Continue cooking for 25 minutes more, until the meat mixture thickens to a Sloppy Joe consistency. Season to taste with more salt and pepper, as needed. Remove from heat and let cool completely.
3. Lightly flour a surface and roll one piece of the puff pastry dough to a thickness of ⅛-inch. Using a pie plate as a rough guide, cut 4 (5¼-inch) circles from the dough. Save the puff pastry scraps for another use. Gently press each dough round into a pie plate. Nest a second, empty pie plate within each dough-lined pie plate and set on a large baking sheet. Place another large baking sheet on top, sandwiching the pie plates, then flip both sheets over so the pie shells are upside down. Set a heavy pan on the top baking sheet. (Alternatively you can blind bake the shells with parchment and pie weights.) Set the baking sheets and pie shells in the oven until the dough is golden, about 20 minutes. Cool shells completely.
4. Increase the oven temperature to 450°. On a lightly floured work surface, roll out the second piece of puff pastry to a thickness of ⅛-inch. Cut 4 (4¾-inch) circles from the dough, saving the scraps for another use. Fill the baked, cooled pie shells with the cooled meat mixture. In a small bowl, whisk together the egg with 1 teaspoon of cold water. Brush the egg wash on the top edges of the baked pie shells. Place a raw dough circle on top of each pie and gently press to seal. Cut a few vents into the top. Brush the tops with more egg wash. Set on a baking sheet and bake until the top is golden, about 15 minutes. Eat warm with more ketchup, if you choose.
