Chop the onions and cut chorizo into desired size pieces. Add to a pot or dutch oven on medium-high heat and cook for about five minutes, stirring occasionally.
Meanwhile, chop the peppers. Add peppers to the pot and cook for another few minutes, stirring often.
Add the diced tomatoes, tomato sauce, chicken broth, garlic, basil, and noodles. Increase the heat to high and bring to a boil. Cook on high/medium high (lower the heat if it starts bubbling too much) for approximately 10 minutes, or until the noodles are softened and the sauce reduces and thickens. I suggest stirring it frequently to ensure that the noodles are all cooked, since the liquid in the pot won't completely cover the noodles as it cooks.
Serve immediately with additional basil, salt & pepper, and freshly grated parmesan cheese if desired.