Cook spaghetti in salted boiling water until just al dente; drain and set aside.
Heat oil in a large skillet over medium; sauté onion and bell pepper 5–6 minutes until softened.
Add garlic, cumin, and chili powder; cook 30 seconds until fragrant.
Stir in tomatoes, chicken broth, and cream; bring to a gentle simmer.
Add shredded chicken and cooked pasta; toss to coat and warm through, 2–3 minutes.
Stir in most of the cheese until melted; season with salt and pepper.
Top with remaining cheese, cover briefly to melt, and garnish before serving.