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1
Preheat oven to 275u00b0F. Mix sugar, pepper, dried thyme, cinnamon, cloves, nutmeg, and 1 tablespoon salt in a small bowl. Place pork in a roasting pan and season with spice mixture. Cover with foil and cook until fork-tender, 3-4 hours. Let pork cool in pan.
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2
Meanwhile, heat butter in a small saucepan over medium heat until foaming, about 5 minutes. Skim foam from surface; discard. Gently simmer butter, skimming foam from surface, until butter is clear (do not let solids brown). Slowly pour clarified butter into a small bowl, leaving solids behind (you should have about 1 cup). Cover and chill until firm, 1-2 hours.
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3
Coarsely shred pork and place in the bowl of a stand mixer fitted with the paddle attachment. Add fresh thyme and 3/4 cup clarified butter and mix on medium-low speed until a coarse but emulsified mixture forms; season with salt. Divide mixture between two 8-oz. jars, packing down. Melt remaining clarified butter in a small saucepan over low heat; pour over mixture. Cover jars. Chill until pork mixture is firm, at least 4 hours.
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4
DO AHEAD:
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5
Heat oil in a large saucepan over medium heat. Add shallots and cook, stirring occasionally, until browned, 8-10 minutes; remove from heat. Add brandy, then return pan to heat and cook shallot mixture until brandy is reduced by half, about 2 minutes. Add garlic, thyme, and broth; cook, stirring occasionally, until shallots are soft and glazed, 25-35 minutes. Remove from heat, discard garlic and thyme, and stir in vinegar and sugar; season with salt. Let cool.
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6
Serve potted pork with braised shallots, toasts, and mustard.
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7
DO AHEAD:
