Heat a Dutch oven or large pot over medium-high heat. Add the ground beef and chopped onion and cook, breaking up the meat, until the beef is browned and the onion is softened, about 5–7 minutes. Drain any excess fat if desired.
Add the garlic and cook, stirring, for about 1 minute until fragrant.
Stir in the Rotel tomatoes, tomato sauce, taco seasoning, beef broth, tomato paste, and Worcestershire sauce. Bring the mixture to a boil.
Add the spaghetti noodles (break them in half if needed to fit). Reduce heat to medium so the mixture simmers gently.
Cook, stirring frequently and scraping the bottom of the pot, until the spaghetti is tender, about 15–18 minutes.
With about 5 minutes remaining, stir in the shredded cheddar and Monterey Jack cheeses until melted and evenly combined.
Remove from heat, garnish with chopped cilantro if desired, and serve immediately.