Heat the oil in a large skillet over medium-high heat. Add the beef and onions and cook, breaking it the meat with the back of a spoon, until it is no longer pink, about 7 minutes. Drain excess fat off of the beef if necessary.
Season the beef with salt, pepper, chili powder, cumin, oregano, and tomato paste. Toss to coat evenly.
Add the pasta, diced tomatoes and green chiles, and chicken broth. Stir to combine.
Bring to a boil, then reduce the heat to a slow steady boil, stirring occasionally, and cook until the pasta is al dente, about 13 minutes. Turn off heat and stir in cheese (if using). Let stand a few minutes before serving.
Garnish with freshly chopped cilantro, sliced avocado, sliced jalapeños, and radishes.