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1
To make the crust, peel the potatoes and cut them into 1 1/2-inch chunks.
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2
Place them in a pot, add water to cover generously and a large pinch of salt, cover, and bring to a boil over high heat.
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3
Boil briskly until the potatoes are a bit beyond fork-tender, almost collapsing, about 10 minutes.
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4
Drain in a colander and, while the potatoes are still moist, return them to the pot.
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5
Let cool briefly until no longer steaming.
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6
Add the milk, butter, and horseradish and mash with a potato masher or sturdy wire whisk until no longer chunky, almost creamy.
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7
Whisk in 1 teaspoon salt and the pepper, taste, and adjust the seasoning with more salt and pepper if desired.
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8
Set aside in a warm place.
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9
Preheat the oven to 400F.
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10
To make the filling, melt the butter in a large saute pan over medium heat.
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11
Add the pearl onions, carrots, and celery, stir to mix, and cook, stirring occasionally, until the vegetables are slightly softened, about 5 minutes.
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12
Add the lamb sausage and continue cooking, stirring to break up the clumps, until no longer pink, 3 to 4 minutes.
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13
Add the thyme, tomato paste, Worcestershire, salt, pepper, and water and stir to mix.
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14
Bring to a boil over medium heat and cook until slightly thickened, about 3 minutes.
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15
To assemble the pie, transfer the filling to a 2-quart baking dish, preferably one that can segue from oven to table for ease of serving.
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16
Spread the mashed potatoes across the top and, with a fork or spoon, lift them into decorative peaks here and there.
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17
Bake until the top is golden around the edges and across the peaks, 30 to 35 minutes.
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18
Serve hot, directly from the baking dish.
