Meanwhile, as the potatoes cook, begin the filling. Preheat the oven to 400°F.
In a 12-inch skillet, heat the vegetable oil until it begins to simmer over medium-high heat. Add the onions, and carrots and cook until they just begin to brown a bit, about 3-4 minutes. Stir in the garlic.
Stir in the lamb or beef, salt, and pepper and saute until the meat is cooked through and no longer has any pink. Drain excess fat (**See Recipe Notes ). Sprinkle the meat mixture with the flour and stir to evenly coat. Cook for 1 minute.
Stir in the tomato paste, chicken broth, Worcestershire, rosemary, and thyme. Bring the mixture to a boil, then reduce the heat and cover, and gently simmer, until the mixture thickens a bit, about 10-12 minutes. Stir in the thawed and well-drained corn and peas.
Pour the filling mixture into an 11x7-inch baking dish. Spread the top evenly with the mashed potatoes, taking care to create a "seal" to the edges of the baking dish.
Place the baking dish on an aluminum foil-lined, rimmed baking sheet. Bake in the middle of the preheated oven until the potatoes begin to brown, and the filling is heated through in the center, about 25-30 minutes. Allow the casserole to cool on a baking rack for 15 minutes before serving.