Place the cubed potatoes in a large pot and cover with cold salted water. Bring to a boil, then reduce heat and simmer for 15 to 18 minutes until fork-tender. Drain well, then mash with the butter, milk, cheddar, and salt until smooth and creamy. Set aside.
While the potatoes cook, heat the olive oil in a large oven-safe skillet over medium-high heat. Add the ground lamb, breaking it up with a spoon, and cook for 6 to 7 minutes until browned. If there is excess fat, drain all but 1 tablespoon.
Add the onion, carrots, and celery to the skillet. Cook for 5 to 6 minutes until the vegetables begin to soften. Add the garlic and tomato paste, stirring for 1 minute until fragrant.
Pour in the beef broth and tamari. Add the thyme and rosemary. Stir to combine and bring to a simmer. Stir the cornstarch slurry and add it to the skillet, cooking for 2 minutes until the filling thickens. Stir in the frozen peas and season with salt and pepper. Remove from heat.
Preheat the broiler to high. Spread the mashed potato topping evenly over the filling, starting from the edges and working inward. Use a fork to create textured ridges on the surface.
Place the skillet under the broiler for 4 to 6 minutes, watching closely, until the potato topping is golden brown with crispy peaks. Let cool for 10 minutes before serving.