Prepare the greens: Wash all of your greens thoroughly in cool water, removing any grit or dirt. Set aside to drain while you start the gumbo base.
Brown the meat: Heat 1 tablespoon of oil in an extra-large pot over medium heat. Add the beef and chicken and cook for 5–6 minutes, stirring occasionally, until just browned.
Add the sausage and ham: Add the sliced sausage and diced ham to the pot. Cook for another 5-6 minutes, or until lightly browned and aromatic.
Sauté the vegetables: Stir in the celery, onion, green bell pepper, and green onions. Cook slowly for about 10 minutes, or until softened and translucent.
Add the garlic and seasonings: Add the minced garlic and cook for 30 seconds, then stir in the flour, cayenne pepper, salt, and black pepper. Cook the flour and spices for 2-3 minutes, stirring continuously.Note: Do not add the filé powder at this stage Wilt the greens: Add about ⅓ of the washed and trimmed greens to the pot and pour in enough water to just cover them. Increase the heat to high and bring to a boil. As the greens begin to wilt and sink, use a spoon to gently push them into the liquid.
Add remaining greens gradually: Continue adding the remaining greens a handful at a time, allowing each batch to wilt before adding more. Once all the greens are in and have wilted down, stir to combine and reduce the heat to maintain a gentle simmer.
Simmer: Add the bay leaves to the pot, then cover and simmer for 1 to 2 hours, or until the greens are tender and the gumbo has developed rich flavor. Stir occasionally and check on the seasoning as it cooks.
Finish with filé powder: Remove the pot from the heat. Stir in the filé powder to thicken slightly and add a subtle earthy flavor. Adjust seasonings to taste.
Serve: Ladle the gumbo over freshly cooked white rice and serve hot.