Start by browning the sausage in the olive oil, separating it into small pieces as it cooks. Brown is flavor. The rendered fat from the sausage will permeate the entire dish!
Next, add the diced onions (or the Creole holy trinity if you go that route) and the diced stems directly to the pot with the sausage and rendered fat. Add ½ tsp of salt to help draw the water out of the aromatics. You should find that there is enough oil and fat to make the aromatic mixture glisten. If it doesn’t glisten, add a bit more oil. Stir frequently, until the aromatic mixture has softened, 5 or 10 minutes.
Stir in the garlic, thyme, paprika, bay leaves, red pepper flakes and a bit of freshly ground black pepper (about 1/4 teaspoon). Allow this mixture to cook for a minute or two.
Add 2 cups of broth to the pot and stir to incorporate. Then add the pulled pork, and use two wooden spatulas or large forks to separate the pork into shreds.
Add the remaining 4 cups of broth to the pot. Turn the heat to high and bring to a boil. Add the greens to the pot in batches. Each batch should quickly wilt, making room for the next batch.
Slowly whisk the roux into the gumbo, a bit at a time. Make sure every bit gets fully incorporated. You can taste for seasoning at this point. The flavor of the roux at this point will not be pleasant. But over the next 30 minutes it will mellow and incorporate with all the other flavors in the gumbo.
Simmer the gumbo for another 30 minutes. Simmering for longer is just fine.
One final opportunity to taste for seasoning. For most gumbos, I usually stir in about 1 tsp of apple cider vinegar at this point, but the Carolina style pulled pork already had some vinegar in its seasoning, and the flavor was already bright. You may find the same. If you are serving with rice, you will want the gumbo to be just barely over-salted, to compensate for the unsalted rice.
Fish out the bay leaves. Plate with rice and garnish with something green – scallions, parsley, oregano are all nice options…