Preheat the oven to 400 degrees F. Put the potatoes in a large saucepan, cover with cold water by 1 inch and season with salt. Bring to a boil, then reduce the heat and simmer until tender, 20 to 25 minutes.
Meanwhile, fill a separate large saucepan with 6 cups water; add the bay leaves, thyme sprigs and 2 teaspoons salt. Bring to a boil. Add the carrots, rutabaga, turnip and leeks; reduce the heat to medium low and simmer until the vegetables are tender, about 10 minutes. Reserve 1 1/2 cups cooking liquid, then drain the vegetables. Discard the bay leaves and thyme. Pat the vegetables dry; set aside.
Melt 2 tablespoons butter in a large skillet over medium-low heat. Add the mushrooms; cook until they release their liquid, 3 minutes. Increase the heat to medium; cook until the liquid is evaporated, 2 to 3 minutes. Sprinkle with the flour, coriander and nutmeg; cook, stirring, 1 minute. Whisk in the reserved cooking liquid and 3/4 cup half-and-half. Bring to a simmer; cook until thickened, 3 minutes. Stir in the carrot mixture, peas and lemon zest and juice. Return to a simmer, then remove from the heat. Season with salt and stir in the parsley.
Drain the potatoes and let cool slightly. Return to the pot and add the curry powder and the remaining 4 tablespoons butter and 3/4 cup half-and-half. Season with 3/4 teaspoon salt and mash well.
Spread the mushroom mixture in a 3-quart baking dish. Dollop the mashed potatoes on top; spread with the back of a spoon. Bake until bubbling around the edges and the topping is browned in spots, about 20 minutes. Let rest 10 minutes before serving.