Pre-heat oven to 350°F (180°C). Heat the oil in a large skillet, then cook beef over medium high heat for 7-10 minutes. Add the onion, carrot and garlic, stir and cook for another 5 minutes. Add the Worcestershire sauce, tomato paste and herbs, cook for 2 minutes more, stirring constantly. Pour in the wine and broth; reduce at a simmer until reduced to a scant 1/2 cup (125 mL) liquid in the pan. Stir in the peas.
Meanwhile, prepare both bags of mashed potatoes according to package instructions.
Spoon the beef mixture into a 9 x 13 (3 L) casserole dish. Spread the mashed potatoes on top of the beef mixture with a spatula, starting from the outside and working in. Rough up the mashed potatoes with a fork and sprinkle with the Parmesan cheese.
Bake until bubbling and golden, about 20 minutes. Let cool slightly before serving.