Peel and cube the potatoes. Boil in salted water for 15–20 minutes until tender. Drain, then mash with butter and milk until smooth. Season with 0.5 teaspoon salt. Set aside.
Preheat oven to 400°F (200°C).
Heat olive oil in a large oven-safe skillet over medium-high heat. Cook the onion and carrots for 5 minutes.
Add the garlic, thyme, and rosemary. Cook 30 seconds. Add the ground beef and cook until browned, about 8 minutes. Drain excess fat.
Stir in the flour and cook 1 minute. Add the tomato paste, chicken broth, Worcestershire sauce, salt, and pepper. Simmer 5 minutes until thickened.
Stir in the frozen peas and corn. Remove from heat.
Spread the mashed potatoes evenly over the filling. Use a fork to create peaks on the surface.
Bake 25–30 minutes until the top is golden and the filling is bubbling around the edges.
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