Instructions

Adjust oven rack to middle position and heat oven to 300 degrees. Sprinkle 1 boneless beef chuck-eye roast, trimmed and tied at 1-inch intervals, all over with 1 tablespoon kosher salt and 2 teaspoons pepper. Heat 3 tablespoons oil in large Dutch oven over medium-high heat until just smoking. Add roast and brown on all sides, about 10 minutes; transfer roast to large plate.
Add 2 quartered onions; 2 carrots, halved crosswise; 1 celery rib, halved crosswise; and 12 smashed and peeled garlic cloves to fat left in pot and cook until onions are just softened, about 5 minutes. Stir in 1 tablespoon tomato paste and cook until fragrant, about 1 minute. Stir in 4 cups water and 2 tablespoons beef bouillon, scraping up any browned bits.
Stir in 1 tablespoon Worcestershire sauce, 2 teaspoons dried oregano, 1 teaspoon fennel seeds, 1 teaspoon coriander, 1 teaspoon granulated garlic, ¼ teaspoon allspice, ¼ teaspoon cinnamon, and ¼ teaspoon red pepper flakes. Nestle roast, 6 thyme sprigs, and 2 rosemary sprigs into pot and bring to boil. Cover pot, transfer to oven, and cook until center of roast registers 195 degrees, 2 to 2¼ hours.
Transfer pot to wire rack, remove lid, and let roast and broth cool completely, about 1 hour. Transfer roast to clean plate and cover with plastic wrap. Using slotted spoon, remove onions, carrots, celery, garlic, and herb sprigs from broth and discard. Refrigerate roast and broth separately until meat is well chilled, at least 8 hours or up to 48 hours.
Remove twine from roast and slice roast in half lengthwise. Place roast halves on cutting board, flat sides down, and slice each half crosswise as thin as possible.
Heat reserved broth in Dutch oven over medium heat to bare simmer. Add sliced meat and simmer until heated through, about 2 minutes. Using tongs, divide meat evenly among 8 hinged ciabatta sandwich rolls, then spoon 2 to 3 tablespoons broth over meat to wet each sandwich. Top each sandwich with about 2 tablespoons Chicago-style giardiniera, plus extra to taste. Serve.