2 pounds beef chuck stew meat, cut into 1 1/2-inch pieces
1 ½ cups Green Seasoning, divided
2 tablespoons hot pepper sauce (such as Matouk's or Grace brand hot pepper sauce), divided
¾ cup turbinado sugar, divided
½ cup vegetable oil, divided
2 cups chopped yellow onion (from 1 large onion), divided
4 garlic cloves, smashed and chopped (4 teaspoons)
½ cup ketchup
¼ cup Worcestershire sauce
3 to 4 cups water, divided, plus more as needed
2 cups canned or frozen pigeon peas (drained and rinsed if canned, thawed if frozen)
2 cups uncooked long-grain white rice
4 teaspoons kosher salt, divided
1 ½ teaspoons black pepper, divided
1 (13.5-ounce) can coconut milk, well shaken and stirred
1 Scotch Bonnet pepper, stem removed
2 fresh bay leaves
Toss together beef with 1/2 cup Green Seasoning and 1 tablespoon of the pepper sauce in a medium bowl until combined; cover and refrigerate for 4 hours.
In a 10-quart pot, stir together 6 tablespoons turbinado sugar and 1/4 cup oil until combined. Cook over medium-high heat, stirring frequently, until sugar turns dark brown and begins to foam, about 4 to 5 minutes. Reduce heat to medium and immediately add marinated beef and any remaining marinade. Cook, turning pieces occasionally, until browned on all sides, about 4 to 5 minutes. Add 1 cup onion, remaining 1 cup Green Seasoning, and garlic and cook until onion is slightly translucent, about 3 to 5 minutes.
Add ketchup, Worcestershire sauce, and remaining 1 tablespoon of pepper sauce and cook over medium heat, stirring occasionally and adding 3 to 4 cups water as needed, a cup at a time, until beef is mostly tender, about 30 to 40 minutes. (The meat should have a little bit of liquid around it; you will know to add more water if the meat starts frying instead of simmering.) Remove pot from heat and transfer beef to a large bowl using a slotted spoon; pour cooking liquid into a separate large bowl. Clean the pot and return to the stove.
Combine remaining 6 tablespoons turbinado sugar and remaining 1/4 cup oil in cleaned 10-quart pot and cook over medium-high heat, stirring frequently, until sugar turns dark brown and begins to foam, about 4 to 5 minutes. Add pigeon peas, rice, and remaining 1 cup onion and cook, stirring constantly, until onions are translucent and mixture is coated with caramelized sugar, about 5 minutes; season with 1 1/2 teaspoon salt and 3/4 teaspoon pepper.
Stir together reserved cooking liquid from the meat with coconut milk, adding water to mixture as needed to equal 8 cups total. Add meat and cooking liquid mixture to rice mixture and bring to a simmer over medium heat. Reduce heat to low and stir in Scotch bonnet and bay leaves; season with remaining 2 1/2 teaspoons salt and remaining 3/4 teaspoons pepper.
Cover and cook until liquid is completely absorbed and rice and beef are tender, about 35 to 40 minutes; serve immediately. (The "bun bun" at the bottom of the pot is a special treat.)