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Preheat oven to 350 degrees F (175 degrees C).
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Lightly grease a baking sheet.
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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.
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Stir in the fennel seed and red pepper flakes, and cook for 1 minute more.
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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.
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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.
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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.