Make the lamb: Set a rack in the center of the oven and preheat to 350°. In a food processor, mix the bread crumbs, seaweed, celery leaves, 1⁄2 teaspoon salt, and a pinch of black pepper. Drizzle in the butter, pulsing until the mixture is moistened and thoroughly combined. Set aside.
Season the lamb generously all over with salt and pepper. In a large skillet over medium-high heat, heat the olive oil. Once hot, add the lamb, leaving as much room between the racks as possible. Cook, turning as needed, until well browned all over, 8-10 minutes total.
Transfer the lamb to a large baking sheet (do not clean out the skillet) with the meat's broader, flatter side facing up. Brush the meat all over with the mustard, then coat generously with the prepared seaweed mixture, pressing all over to help it adhere and concentrating most of the mixture on the broad side (discard any crumbs that do not adhere). Cover the bones with foil.
Roast the lamb until the bread crumbs are crispy and the meat feels firmer to the touch, 15-18 minutes for medium-rare. If desired, broil until the top of the coating is lightly browned, 2-3 minutes more. Remove and let the meat rest 5 minutes.
Meanwhile, make the sauce: Heat the drippings in the reserved skillet over medium-high heat. Add the shallot and cook, stirring, until softened, 2 minutes. Add the garlic and cook, stirring constantly, until fragrant, 30 seconds to a minute. Stir in the tomato paste and cook 30 seconds more. Pour in the wine and raise the heat to high; cook, scraping up any browned bits from the bottom of the pan, until the wine is almost completely evaporated, 2-3 minutes. Add the stock and continue to cook over high heat until reduced by two-thirds, 3-4 minutes. Add the butter and cook, stirring or whisking constantly, until melted. (Sauce should be thick enough to coat the back of a spoon.) Taste and adjust the seasoning if needed. Strain the sauce if desired and set aside.
Slice the lamb between the bones to separate the chops. Pour the sauce onto a large platter, then nestle the lamb chops into the sauce and serve immediately.