1. Preheat oven to 375 degrees.

2. Place 2 tablespoons oil in a Dutch oven large enough to hold the ribs in a single layer, over medium heat. When oil is hot, add onions, carrots, leeks, and 1 teaspoon salt. Cook, stirring occasionally, until vegetables are soft, about 15 minutes. Add garlic, 2 tablespoons coriander seeds, peppercorns, thyme, rosemary, and bay leaves.

3. Using kitchen twine, tie meat on each rib securely to the bone. Season the short ribs with 1 teaspoon salt and add them to the Dutch oven. Add enough water to the pan to just cover the ribs and bring to a simmer. Transfer pan to the oven. Simmer ribs, turning them every 30 minutes until very tender, about 2 hours. Remove pan from oven and allow ribs to cool in their liquid. Strain to remove vegetables, cover, and refrigerate, with meat still in its liquid, overnight.

4. Grind together remaining 1 1/2 tablespoons coriander seeds with celery salt, Aleppo pepper flakes, allspice, and cumin in a spice grinder or mortar. Transfer spice mixture in a shallow dish; set aside.

5. Remove meat mixture from refrigerator; skim and discard any accumulated fat from the surface. Remove short ribs from liquid. Transfer liquid to a medium saucepan and bring to a boil over medium-high heat. Cook until liquid is reduced by half, about 10 minutes.

6. Cut meat from bones. Pat meat dry with a paper towel, then trim off any excess fat or cartilage. Slice meat across the grain into 3/8-inch-thick medallions. Dredge each slice in spice mixture. Place remaining 2 tablespoons oil in a large skillet over medium-high heat. Season meat with 1/2 teaspoon salt. When oil is hot, add meat to pan. Brown meat for 1 to 2 minutes and turn; add butter. Continue browning meat, basting regularly with butter. Transfer meat to a paper-towel-lined plate to drain, then arrange on warmed serving plates. Serve each with mashed potatoes and 1 to 2 tablespoons of the reduced braising liquid.