Heat oil in a large, heavy pot over medium heat until hot; add onion, bell peppers and garlic. Season generously with salt (about 1 teaspoon). Cook, stirring often, until peppers are soft and their juices have reduced and thickened to a sweet syrup (about 15 minutes).
Stir in mustard seeds, paprika, pepper flakes, thyme, beans, tomatoes, and 6 cups (1 1/2 quarts) water. Season generously with salt (about 2 teaspoons).
Cover and bring to a boil. Reduce heat and simmer soup, covered, until beans are tender but haven’t yet begun to break apart (about 40 minutes).
Stir in basil. Season soup with additional salt to taste. Stir in corn kernels, if using. Remove thyme stems before serving.
Before her diagnosis, Caroline wrote a book on cakes called Cake Magic!. She started developing a birthday cake using her gluten-free mix found in that book. Check out other recipes she’s developing for her new life—and the stories behind them—on her blog, The Wright Recipes. Her next book, Soup Club, is a collection of recipes she made for her underground soup club of vegan and grain-free soups she delivers every week to friends throughout Seattle's rainy winter. (Available February 2021.)