Place the diced tomatoes with green chiles in a small food processor or blender and pulse until slightly blended but still chunky; set aside.
Heat the oil in a large Dutch oven or stockpot over medium-high heat.
Add the ground meat and minced onion and sauté, breaking the meat into bite-sized pieces, until browned and cooked through; drain excess grease if needed.
Return the pan to the heat and stir in the taco seasoning, blended tomatoes, tomato sauce, and 2½ cups water; bring the mixture to a boil.
Once boiling, add the broken spaghetti, reduce heat to medium, and simmer uncovered, stirring often, until noodles are al dente, about 15–18 minutes; add additional water in 1/4-cup increments if the liquid evaporates too quickly (usually up to 3 cups total).
When the pasta is tender, remove the pot from heat and stir in the grated cheddar; let sit a few minutes to melt the cheese.
Serve hot topped with chopped cilantro and any desired toppings such as sour cream, avocado, tomato, green onion, jalapeño, or black olives.