Pulse the scallions, thyme, garlic, 1 teaspoon each salt and pepper, the celery seeds and allspice in a food processor to make a paste. Pierce the roast all over with a paring knife; rub the spice paste into the meat. Tie the roast with kitchen twine so it keeps its shape.
Spread the carrots in a 6-quart slow cooker and set the roast on top. Insert an instant-read thermometer at an angle into the center of the roast; position the thermometer so it can be easily read through the lid of the slow cooker.
Combine 1 1/2 cups water, the Worcestershire sauce and bouillon cube in a microwave-safe bowl; microwave until hot, 2 to 4 minutes. Add to the slow cooker. Cover and cook on low until the meat registers 120 to 130 degrees F for medium rare, about 2 hours. Transfer the meat to a cutting board and cover with foil; let rest 15 minutes. Skim off the excess fat from the cooking liquid.
Remove the twine and slice the meat very thinly. Spoon some cooking liquid onto the cut sides of each roll; sandwich with the meat, horseradish and/or mustard. Serve with more cooking liquid for dipping.