Place the potatoes in a medium-sized saucepan and add cold water to cover. Salt the water, then place over high heat until the water simmers. Lower the heat to medium-high and continue to simmer, partially covered, until the potatoes are very tender, about 20 minutes.
Meanwhile, spray a large skillet with nonstick cooking spray and heat over medium high heat. Add the lamb and cook, stirring frequently to break up the meat, until brown and crumbly, about 5 minutes. Turn into a colander and carefully wipe out the skillet.
Heat 2 tablespoons of the butter in the same large skillet over medium high heat, and when it is melted, sauté the onion, carrots, celery, fennel, garlic and thyme and sauté for 4 to 5 minutes until the vegetables are lightly golden and tender. Add the flour and stir until it coats the vegetables about 1 minute. Stir in the lamb, and then 1/2 cup of the milk and the broth and cook until the liquid thickens and coats the mixture as sauce, stirring occasionally, about 4 minutes. Stir in the corn and peas, and season with salt and pepper. Add the Worcestershire sauce and continue cooking until everything is well combined and hot, about 3 minutes. Turn the mixture into a 9-inch deep dish pie pan.
Drain the cooked potatoes. In the saucepan you used to cook the potatoes, heat the remaining 3/4 cup milk and the remaining 2 tablespoons butter until barely simmering. Put the cooked potatoes through a food mill, a ricer, or use a potato masher to mash and add them to the simmering milk. Stir in the cheddar and havarti, season with salt and pepper and stir to blend well, until the cheese is melted and incorporated. Spread the mashed potatoes evenly over the lamb mixture in the pie pan. Use a spoon to make nice wavy peaks and valleys in the potatoes; the peaks will then get nicely browned and beautiful in the baking.
Bake for 15 minutes until the top is set and a bit colored. If you want the top a bit more browned you can run it under the broiler for a minute or two, but keep a close eye on it so it doesn’t get too brown. Remove from the oven and let sit for 5 to 10 minutes before serving.