Heat oil in a large Dutch oven. Brown meat for about 5 minutes. Push meat aside and add onion, garlic, carrot, and celery. Sauté for 3 to 4 minutes. Stir in dried basil and thyme.
Add stewed tomatoes. Pour in apple juice and beans. When liquid comes back to a boil, season with salt and pepper. Reduce heat to low and simmer for about 1¼ hours.
Prepare the roux while stew is simmering. Melt butter in a small sauce pan over medium heat. Stir in flour and cook till smooth, about 2 to 3 minutes.
When stew is ready, ladle about a cup of hot liquid into the roux and mix till smooth. Pour the mixture back into Dutch oven, gently stirring until thickened.
Turn off heat and serve warm with rice or crusty bread.