Heat your Blackstone griddle or a large skillet over medium-low heat and add the oil. Slowly whisk in the flour to make a roux, stirring constantly until it turns a deep chocolate brown with a nutty aroma. This can take 20–30 minutes and must not be left unattended.
Bring the chicken stock to a simmer in a large pot, then carefully transfer the roux into the stock, stirring well to combine.
Season the alligator meat with Cajun spices and brown it on the griddle. Brown the andouille sausage slices as well, then add both meats to the gumbo pot.
Sauté the okra on the griddle until lightly browned, then add the onion, bell pepper, and celery and cook until softened. Transfer all the vegetables into the gumbo pot and stir to blend with the roux and stock.
Reduce the heat to low and let the gumbo simmer gently for 1½–2 hours, stirring occasionally and adding water if needed to maintain consistency. Adjust seasoning with more Cajun spices, salt, and black pepper as desired.
Spoon the gumbo over a bed of white rice and serve hot. The flavors deepen even more if enjoyed the next day.
