In a large resealable container, combine 3 tablespoons flour, salt and pepper. Add beef in batches; shake to coat. Invert a 10-in. cast-iron or other ovenproof skillet onto parchment; trace circle around pan 1/4 in. larger than rim. Cut out circle and set aside. In same skillet, saute beef in oil until browned. Add onion and garlic; cook and stir until onion is tender. Add wine, stirring to loosen browned bits., Combine 1-1/2 cups broth, tomato paste, Italian seasoning and basil; stir into skillet. Add bay leaf. Bring to a boil. Reduce heat; cover and simmer until meat is tender, about 45 minutes. Add potatoes and carrots; cook until vegetables are tender, 20-25 minutes longer., Meanwhile, roll out puff pastry to fit skillet, using parchment circle as a guide; cut venting slits in pastry. Keep chilled until ready to use. , Combine the remaining flour and broth until smooth; gradually stir into skillet. Bring to a boil; cook and stir until thickened and bubbly, about 2 minutes. Discard bay leaf. Stir in peas and parsley. , Brush beaten egg around edge of skillet to help pastry adhere; carefully place pastry over filling. Using a fork, press pastry firmly onto rim of pan; brush with egg. Bake pie at 425° until pastry is dark golden brown, 30-35 minutes. Let stand for 10 minutes before serving.