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1
Combine all ingredients except pork and oil in a medium sauce pan. Place over medium-high heat, bring to a simmer, and cook until salt is dissolved. Cool to room temperature.
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2
Put the roast in a gallon zippered plastic bag, add brine, evacuate most of the air, and refrigerate for 18 - 24 hours - turning three or four times while brining to distribute the brine.
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3
Allow roast to warm on the counter for 2 to 3 hours before cooking.
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4
Heat oven to 250F. Rinse roast and pat dry with a lint-free kitchen towel. Discard brine.
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5
Heat oil in a heavy, oven-proof skillet over medium-high heat. Add roast and brown well on 3 sides - about 3 minutes per side. When you flip the fourth side down, place the skillet in the center of the oven. If the roast has a fatty side brown it first and end with it on top.
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6
For tender, medium-rare meat, cook roast to 145-150 degrees at its center according to an instant-read thermometer, 1 to 1 1/2 hours. Alternatively, for cooked through, succulent meat, cook to 165-170 degrees (we don't advise going for something in between). Remove from oven, place on a cutting board, and tent with foil.
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7
Heat a large skillet over medium heat. (Unfortunately the fond that accumulates in the bottom of the roasting skillet is too salty to use in a sauce, so use another large skillet.) Add butter and swirl to melt.
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8
Add apples and rosemary in a single layer and lightly browned - about 5 minutes. Flip and brown other side. Add minced onion and cook 1 minute longer.
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9
Add rum and reduce by half. Add cider and reduce by half. Taste and season with salt and pepper (light on the salt).
