To prepare brine, combine 3 cups water, 1/4 cup salt, 2 tablespoons sugar, peppercorns, coriander seeds, quartered plum, and garlic in a large Dutch oven; bring to a boil, stirring until salt dissolves. Remove from heat; cool completely. Stir in 2 1/2 cups sake. Add pork to sake mixture; weight pork down with a small clean plate. Cover and refrigerate 8 hours or overnight.
To prepare glaze, combine 1/2 cup sake, juice, 2 tablespoons sugar, 1/8 teaspoon salt, and chopped plums in a saucepan; bring to a boil. Cover, reduce heat, and simmer 10 minutes or until plums are very tender. Place mixture in a food processor, and process 1 minute or until smooth. Return to pan, and simmer until reduced to 1 cup (about 10 minutes). Remove and reserve 1/2 cup glaze.
Preheat oven to 400°.
Remove pork from brine; discard brine. Place pork on the rack of a broiler pan coated with cooking spray; pat pork dry with paper towel. Sprinkle pork with pepper. Baste with 1/4 cup glaze. Bake at 400° for 20 minutes. Remove from oven; baste with 1/4 cup glaze. Return to oven, and bake 20 minutes or until thermometer registers 155°. Remove from oven; let stand 10 minutes before thinly slicing. Combine reserved 1/2 cup glaze and 1 tablespoon hot water; stir well. Serve with pork.