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Sprinkle pork with salt and black pepper.
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Heat oil in a large skillet over high heat. Sear pork until browned, about 3 minutes per side. Transfer to a slow cooker.
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Using the same skillet, reduce heat to medium; cook shallots, stirring, until they begin to soften, 3 to 4 minutes. Add vinegar and cook, stirring and scraping up any browned bits, until liquid is nearly evaporated.
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Pour shallot mixture over pork in slow cooker. Add cider, garlic, and bay leaf. Cover and cook on low for about 6 hours until it is fork tender. Transfer roast to a plate and cover loosely with foil.
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Pour remaining liquid through a fine-mesh strainer into a large saucepan over high heat; discard bay leaf and other solids. Bring to a boil, then reduce heat and cook, skimming fat from top, until reduced to ¼ original volume.
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Remove from heat and slowly stir in mustard and cayenne. Slowly add cold butter, whisking until each addition is incorporated. Sprinkle in thyme and season with salt and black pepper.
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Shred or cut pork into slices. Serve with sauce.