Place the oil in a large heavy pot (such as a Dutch oven) over medium heat. Add the onion, carrots, and a large pinch of salt and cook, stirring now and then, until the vegetables are beginning to soften, about 5 minutes. Add the garlic, tomato paste, and dried oregano and cook, stirring until very fragrant, about a minute.
Add the cabbage, beans, diced tomatoes with their juice, and the broth, turn the heat to high, and bring the mixture to a boil. Season to taste with salt. Reduce the heat to low and simmer, uncovered, until the cabbage is softened and the flavors are very well combined, at least 30 minutes (but it’s fine for up to an hour over very low heat, if that helps to know). Just before you’re ready to eat, add the pasta and cook until softened, about 10 minutes or so.
Serve the soup hot with lots of grated cheese, freshly ground black pepper, a spoonful of pesto, and/or a shower of Haley’s Savory Sprinkles in each bowl.