Combine 5 cups cold water, salt, soy sauce, honey, garlic, and ginger in a large bowl, stirring to dissolve salt and honey. Submerge pork roast in brine. Cover and refrigerate at least 18 hours or up to 24 hours.
Preheat oven to 300°F with rack in center of oven. Remove pork from brine, and discard brine. Pat pork dry with paper towels; place pork on a small rimmed baking sheet lined with aluminum foil. Let pork stand at room temperature while oven preheats.
Stir together honey, mustard, ginger, and salt in a small bowl until well combined.
Brush 1 tablespoon glaze over pork. Roast pork in preheated oven until an instant-read thermometer inserted in center of roast registers 125°F, about 45 minutes, brushing pork with an additional 1 tablespoon glaze after about 20 minutes. (Internal temperature of pork will continue to rise during broiling and resting.)
Stir together parsley, oil, ginger, vinegar, garlic, and salt in a medium bowl until combined. Season with additional vinegar to taste. Scatter half of the parsley sauce (about 2/3 cup) on a serving platter; set remaining sauce aside.
Remove pork from oven; increase oven temperature to broil. Brush pork with remaining glaze (about 1 tablespoon). Return pork to center rack in oven, and broil until glaze browns and caramelizes in spots and a thermometer inserted in center of roast registers 140°F, 8 to 10 minutes. Remove pork from oven, and transfer to a large cutting board, reserving drippings in pan. Tent pork with foil, and let rest 10 minutes.
Cut pork into thin slices, and arrange on parsley sauce on platter. Pour reserved drippings from cutting board and pan into bowl with remaining sauce; stir to combine. Spoon evenly over pork. Serve immediately.