Heat 2 tablespoons of the oil in a large Dutch oven over medium-high heat. Add the pork cubes in a single layer and brown on all sides, about 6-8 minutes total. Remove the pork to a plate and set aside.
Add the remaining tablespoon of oil to the pot. Stir in the onion and cook until softened, about 4 minutes. Add the garlic and cook for 1 minute more.
Sprinkle the flour over the onions and garlic. Stir constantly for 2 minutes to form a light roux that will thicken the gravy.
Slowly pour in the beef broth while stirring to avoid lumps. Add the diced tomatoes, thyme, bay leaf, and the browned pork. Season with salt and pepper.
Bring the mixture to a simmer, then reduce the heat to low. Cover and cook for 45 minutes, stirring occasionally, until the pork is tender and the gravy has thickened.
Stir in the sliced okra. Cook uncovered for 10-12 minutes until the okra is tender but still holds its shape. Remove the bay leaf before serving.