Trim pork shoulder of excess fat and cut lengthwise into 3 even pieces. Place pieces into a sealable bag.
Whisk together 3 tbsp of honey and the remaining ingredients. Pour marinade over pork and seal bag. Lay bag flat on a small tray or shallow baking pan and refrigerate for at least 24 hours, flipping at least once.
Preheat oven to 325°F and place rack in the middle. Line a baking tray with tin foil and parchment. Drain marinade into a shallow skillet and place pork onto the baking tray. Bake for 30 minutes, turn pork and continue baking for 30 minutes.
Meanwhile, whisk the remaining 2 tbsp of honey into the marinade and reduce over medium-high heat until it coats the back of a spoon, about 7-8 minutes.
Increase oven temperature to 350°F. Generously baste pork with sauce and bake for 10 minutes. Turn pork, baste and bake for 10 minutes.
Turn oven to broil and remove parchment paper from under the pork to the clean tin foil beneath (see notes). Baste pork and broil for 1-2 minutes, turn pork, baste and broil for 1-2 minutes. Remove from oven, cover and allow to rest for 10 minutes before slicing.