Eula Mae Dore is a legend on Avery Island. She recently retired as proprietor of the Tabasco deli, where she served wonderful sandwiches and salads to the workers who dropped in for lunch.
Heat 1/2 cup of the oil in a large skillet (not cast iron) over medium heat and add the okra. Cook, stirring frequently, until it is no longer ropy, about 30 minutes. Add the vinegar and cook, stirring, for another 10 minutes, until the okra takes on a brownish color and is reduced to about a quarter of its original volume. Put the okra in a medium bowl and set aside.
In a large stockpot over high heat, bring the water to a boil. Meanwhile, add the remaining 1/4 cup oil and the ham to the skillet. Saute the ham over medium-high heat for about 10 minutes, or until it is lightly browned.
With a slotted spoon, remove the ham to the stockpot. In the same skillet, combine the onions, celery, garlic and pepper; cook, stirring constantly, for 10 minutes, until the vegetables are tender. Add the vegetables, okra and tomatoes to the stockpot; cover and simmer over medium heat for 1 hour.
Reduce the heat to very low, add the shrimp and simmer very slowly for 10 minutes. Add the crabmeat and Tabasco sauce; simmer for an additional 5 to 10 minutes. Serve the gumbo in soup bowls with scoops of rice.