Cut smoked sausage into slices that are about ⅛-inch. Cook over medium heat in a Dutch oven. Remove from the Dutch oven and drain well on paper towels. Pour fat from the Dutch oven.
Heat one tablespoon of olive oil in the same Dutch oven used to cook the sausage. Add the onions, celery, and bell pepper. Cook over medium heat, scraping up the browned bits from the bottom of the Dutch oven, for about 10 minutes or until tender.
Stir in minced garlic, Creole seasoning, salt, pepper, and thyme. Cook for 30 seconds or until the garlic is fragrant.
Stir in uncooked rice; cook for about 2 minutes. Add undrained petite diced tomatoes; stir to combine. Continue scraping up browned bits from the bottom of the Dutch oven.
Add chicken broth and cooked sausage; stir to combine. Bring to a boil. Cover the Dutch oven with a paper towel and lid. Reduce heat to medium-low. Cook for 15 minutes.
Remove the lid and paper towel. Add rinsed and drained black-eyed peas; stir to combine. Cover the pan with a clean paper towel and lid. Cook for an additional 10 minutes or until the rice is done.
Remove the paper towel and lid. Let the jambalaya sit for five minutes. Fluff with a fork and serve.
Yield: 8 servings.