Dice the sausage into 1/2-inch rounds, then finely chop the onion and celery stalks. Mince the garlic cloves, peel and cut the potatoes into 1/2-inch cubes, and roughly chop the cabbage into 1-inch pieces. Measure out all spices (salt, black pepper, red pepper flakes, bay leaf) into a small bowl. Having everything prepped and ready will make the cooking process smooth and prevent overcooking any components.
Heat a large heavy-bottomed pot (at least 5-6 quarts) over medium-high heat. Add the diced sausage and cook for 3-4 minutes, breaking it up slightly as it browns, until some fat is rendered and the sausage develops color. Add the chopped onion and celery, cooking for 2-3 minutes until they begin to soften and become fragrant. Stir in the minced garlic and cook for just 30 seconds to bloom its flavors without burning it. This layered approach to building aromatics creates a deeper, more complex base than cooking everything together from the start.
Pour in the diced tomatoes (with their juice), tomato sauce, and beef broth, then add the rice, diced potatoes, and chopped cabbage. Sprinkle in the salt, black pepper, red pepper flakes, and bay leaf, stirring well to combine and distribute the spices evenly throughout the pot. Bring the mixture to a boil over medium-high heat, stirring occasionally—this ensures the rice cooks evenly and the spices are fully incorporated into the liquid.
Once the mixture reaches a boil, reduce the heat to medium-low, cover the pot with a lid, and simmer for 35-40 minutes. The rice should be tender and have absorbed most of the liquid, and the potatoes should be fork-tender. I like to give it a gentle stir around the 20-minute mark to prevent the rice from sticking to the bottom, but avoid stirring too much as it can make the rice mushy. The jambalaya is ready when there's just a small amount of liquid remaining and everything is cooked through.
Remove the pot from heat and let it rest uncovered for 2-3 minutes—this allows the rice to finish absorbing any remaining liquid and makes the texture more cohesive. Give the jambalaya a final stir, taste, and adjust seasonings if needed. Remove the bay leaf, then ladle into bowls and serve hot.