Preheat your oven to 350°F (180°C).
Heat oil in a large skillet over medium-high heat. Add onions and ground beef or lamb; cook until browned, about 5 minutes. Drain any excess grease if necessary.
Add carrots, corn, peas, Worcestershire sauce, salt, and pepper. Cook until vegetables are tender, approximately 5 more minutes. Stir in flour and cook for an additional 1-2 minutes until the mixture thickens.
Transfer the meat and vegetable mixture to a 9-inch pie dish, spreading it evenly.
Boil potatoes in salted water until tender (about 15 minutes), then drain and mash with butter until creamy. Spread the mashed potatoes over the top of the meat and vegetable mixture in an even layer.
Bake in the preheated oven for 25-30 minutes, or until the top turns golden brown.
Allow the pie to cool slightly before serving to allow the flavors to meld together harmoniously.