Rinse the corned beef brisket under cold water to remove excess salt and pat dry with paper towels.

Fill a large heavy-bottomed pot with 4 quarts of water and bring to a rolling boil over high heat, about 8 to 10 minutes.

Carefully lower the corned beef into the boiling water, add the bay leaves, peppercorns, and smashed garlic cloves, and return to a boil.

Reduce heat to low, cover the pot slightly ajar, and simmer gently for 1 hour and 45 minutes.

Add the red potatoes and carrots to the pot and continue simmering for 30 minutes.

After 15 minutes, add the pearl onions and cabbage wedges and simmer for an additional 15 to 20 minutes.

Pierce the beef with a fork to check tenderness—it should shred slightly under gentle pressure—and ensure the vegetables are fork-tender.

Use tongs to remove the corned beef from the pot and let it rest on a cutting board for 5 to 10 minutes.

Slice the beef against the grain into quarter-inch thick slices, arrange on a platter with the vegetables, and ladle hot broth over everything.