In a dutch oven, heat the EVOO over medium heat. Add the sausage, onion, celery, bay leaf, thyme and cayenne; season with salt and pepper. Cook, stirring occasionally, until the onion is golden, 10 to 12 minutes. Stir in the garlic and cook for another 30 seconds.
Using a fork, mash 1/2 cup beans and add them to the pot. Add the remaining beans and the stock; bring to a boil. Reduce the heat to medium-low and simmer, stirring occasionally, until thickened, about 20 minutes. Discard the bay leaf.
Meanwhile, in a medium saucepan, combine the rice and 2 cups water. Cover and cook over medium-low heat until the water is absorbed and the rice is cooked through, 20 to 22 minutes. Remove from the heat and cover for 5 minutes; fluff with a fork.
Divide the rice among individual bowls. Serve with the beans and sausage; top with the celery leaves.