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Step 1
Rinse the meat, blot it dry, and bring it to room temperature. Take a good look at the meat, and if it is not compact and even, tie it into a neat bundle using kitchen twine. Set it aside. Choose a lidded container large enough to hold the pork and the brine inside.
Step 2
Mix together the kosher salt, brown sugar, cloves, and just enough hot tap water to dissolve the salt and sugar. Pour that liquid over the meat in the container, and add cold water to cover. Let the meat sit, refrigerated, all day or overnight. When you are ready to cook, remove the meat from the brine, rinse it well, and blot it dry. Lightly salt and pepper the meat and place it on a rack in a roasting pan, fat side up.
Step 3
Melt the butter over low heat and gently cook the garlic until fragrant, but not colored. Pour this over the meat and let it sit at room temperature for 1 hour.
Step 4
Heat the oven to 350°F. Roast the meat for 30 minutes. Reduce the heat to 300°F and begin basting the meat with the vermouth every 20 minutes or so. The meat should cook for at least 20 minutes per pound, about 1 additional hour, or until it registers an internal temperature of 150°F on an instant-read thermometer.
Step 5
Let the meat rest for at least 15 minutes before slicing it and serving it with the pan juices.