Bring a large saucepan of salted water to a boil. Add the pearl onions and blanch for about 1 minute, or until the skins start to loosen. Drain into a colander and run under cold water until cool to the touch.
Heat the oven to 400°F and arrange a rack in the upper third. Trim ends from the onions, cut in half, and peel. Heat butter in a Dutch oven or a large, heavy-bottomed pot with a tightfitting lid over medium heat. When it foams, add onions, leeks, and garlic, season with salt and freshly ground pepper, and cook until leeks are soft. Add carrots, celery, and thyme and cook until the vegetables are just getting tender. Add flour, stirring until it is well incorporated, about 1 minute. Deglaze the pan with the white wine and cook 1 minute more.
Add broth and turkey. Bring mixture to a simmer, cover, reduce heat to low, and cook, stirring frequently, until vegetables are tender and sauce has thickened slightly, about 15 minutes. Season with salt and pepper if necessary.
Transfer mixture to a 13-by-9-inch baking dish and spread mashed potatoes over the top. Bake until filling is hot and top is browned, about 35 to 45 minutes.
Beverage pairing: Joseph Drouhin Rully Blanc, France. An unpretentious dish like shepherd’s pie with turkey calls for a wine that’s simple, thirst-quenching, and refreshing. A village white Burgundy, with its lemony, mineral, and floral notes, will be an unassuming but satisfying companion.
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