Step 1

Stir together first 5 ingredients; rub over pork. Roll pork up, and tie with kitchen string. Chill pork, uncovered, 8 to 12 hours.

Step 2

Preheat oven to 325°. Let pork stand at room temperature about 20 minutes.

Step 3

Cook pork in hot oil in a large Dutch oven over medium-high heat 12 minutes, browning on all sides. Remove from Dutch oven; wipe Dutch oven clean. Boil broth and next 2 ingredients in Dutch oven over medium-high heat. Reduce heat to medium, and whisk in mustard; simmer, stirring occasionally, 5 minutes.

Step 4

Return pork to Dutch oven, and add bay leaves. Cut 1 apple into thick slices. Place onions, garlic, and apple slices around pork. Return to a simmer over medium heat. Place a piece of parchment paper directly on pork mixture, and cover Dutch oven with a tight-fitting lid.

Step 5

Bake at 325° for 3 1/2 to 4 hours or until meat is very tender and pulls away from bone. Let pork stand in Dutch oven, covered with parchment paper and lid, at room temperature 30 minutes.

Step 6

Discard parchment paper. Carefully transfer pork to a serving platter; cover with aluminum foil. Skim fat from cooking liquid, and pour cooking liquid through a fine wire-mesh strainer into a large saucepan, discarding remaining solids. Bring to a simmer over medium-high heat. Cut remaining apple into thin slices, and add to mixture. Simmer, stirring occasionally, 5 minutes or until sauce reduces slightly. Remove from heat. Add butter and vinegar, and stir until butter melts and sauce is smooth. Serve sauce with pork.