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1. Dissolve 1/4 cup salt and sugar in 2 quarts cold water in large container. Submerge roast in brine, cover, and refrigerate for at least 1 1/2 hours or up to 2 hours. Remove roast from brine and pat dry with paper towels.
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2. Adjust oven rack to middle position and heat oven to 275 degrees. Bring salt pork and 1/2 cup water to simmer in Dutch oven over medium heat. Simmer until water evaporates and salt pork begins to sizzle, 5 to 6 minutes. Continue to cook, stirring frequently, until salt pork is lightly browned and fat has rendered, 2 to 3 minutes. Using slotted spoon, discard salt pork, leaving fat in pot.
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3. Increase heat to medium-high, add roast to pot, and brown on all sides, 8 to 10 minutes. Transfer roast to large plate. Add milk, garlic, sage, and baking soda to pot and bring to simmer, scraping up any browned bits. Cook, stirring frequently, until milk is lightly browned and has consistency of heavy cream, 14 to 16 minutes. Reduce heat to medium-low and continue to cook, stirring and scraping bottom of pot constantly, until milk thickens to consistency of thin batter, 1 to 3 minutes longer. Remove pot from heat.
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4. Return roast to pot, cover, and transfer to oven. Cook until meat registers 140 degrees, 40 to 50 minutes, flipping roast once halfway through cooking. Transfer roast to carving board, tent with aluminum foil, and let rest for 20 to 25 minutes.
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5. Once roast has rested, pour any accumulated juices into pot. Add wine and return sauce to simmer over medium-high heat, whisking vigorously to smooth out sauce. Simmer until sauce has consistency of thin gravy, 2 to 3 minutes. Off heat, stir in 2 tablespoons parsley and mustard and season with salt and pepper to taste. Slice roast into 1/4-inch-thick slices. Transfer slices to serving platter. Spoon sauce over slices, sprinkle with remaining 1 tablespoon parsley, and serve.
