Place the diced tomatoes with green chiles in a small food processor or blender and pulse until mostly smooth; set aside.
Heat 1 teaspoon oil in a large Dutch oven or stockpot over medium-high heat.
Add the ground meat and minced onion and cook, breaking the meat into bite-sized pieces, until browned and cooked through, about 6–8 minutes; drain excess fat if necessary.
Return the pot to the heat and stir in 2 tablespoons taco seasoning, the blended tomatoes, the 8‑oz can of tomato sauce, and 2 1/2 cups water; bring to a boil.
Once boiling, add the broken spaghetti, reduce heat to medium, and simmer uncovered, stirring often, until the pasta is al dente, about 15–18 minutes. Add additional water in 1/4 cup increments if liquid is evaporating too quickly (you may need about 3 cups total).
When the noodles are tender, remove the pot from heat and stir in the grated cheddar until melted; let sit a few minutes to finish melting.
Serve topped with chopped cilantro and desired toppings such as sour cream, avocado, tomato, green onion, jalapeño, or black olives.