Preheat the oven to 375°F. On a large sheet of parchment paper, roll out the puff pastry to fit inside a 3-qt. baking dish. Place the beef, onion, and peas and carrots in a 3-qt. baking dish; set aside.
In a large skillet, heat 2 Tbs. olive oil over medium-high heat. Add the mushrooms and thyme and cook, stirring occasionally, until the mushrooms are tender and release their liquid. Stir in the flour. Cook and stir 1 minute. Whisk in the stock and salt. Cook and stir until thickened and bubbly, about 5 minutes. Pour sauce mixture over beef mixture in the baking dish; stir gently.
Top with the prepared puff pastry. Cut a few slits in the pastry. Brush with the egg mixture. Bake for 40 to 45 minutes, or until the pastry is golden brown and filling is bubbly.