Cook spaghetti noodles in a large pot of boiling salted water until al dente. Drain.
Meanwhile, heat a large skillet over medium-high heat and add the oil.
Add onions and peppers, cooking and stirring until softened, about 3-4 minutes.
Add chicken breast cubes and cook until white on the outside (they don't necessarily need to brown.
Stir in garlic, salt, chili powder and paprika and cook 1 minute.
Add flour and stir until no white remains.
Stir in broth and milk and bring to a simmer. Reduce heat to medium and cook and simmer until thickened. Stir in shredded cheese and pour over cooked pasta.
