Preheat oven to 350 degrees F (175 degrees C). Lightly grease a baking sheet.
Heat the vegetable oil in a skillet over medium heat. Stir in the onion, fennel, and garlic. Cook and stir until the fennel is tender, and the onion has softened and turned translucent, about 5 minutes. Stir in the fennel seed and red pepper flakes, and cook for 1 minute more. Meanwhile, beat the egg in a bowl, then mix in the ground beef, bread crumbs, parsley, and salt. Add the cooked vegetable mixture, and stir until combined.
Separate the crescent roll dough into two squares. Divide the meat mixture among the crescent roll squares, then seal the dough around the meat. Place seam-side-down onto the prepared baking sheet.
Bake in the preheated oven until the pastry has turned golden-brown, and the center of the pastries registers 160 degrees F (71 degrees C) on a kitchen thermometer, about 30 minutes. Slice and serve.