In a large pot, add oil (2 tablespoons) and heat until it's shimmering. Add onion (1 cup), and sauté over medium heat until onion is translucent. Add garlic (4 cloves) and continue to cook until fragrant, stirring so the garlic doesn't burn for about 1 minute.
Stir in Ortega chiles (1 can), taco seasoning (1 envelope), and oregano (2 teaspoons).
Add the ground beef (1 pound) and brown lightly, breaking it apart with a wooden spoon as it cooks, until there is no pink in the meat.
Add the beef broth (2 cups), and tomato sauce (1 -15-ounce can) to the skillet and stir to mix.
Stir in the pasta (8 ounces) and cover, increasing the heat to medium-high. Cook the mixture, stirring often and adjusting the heat to maintain a vigorous simmer (not a boil). Continue to cook until the pasta is tender, about 9-12 minutes.
Turn the heat to low and add 1 1/2 cups of jack cheese and heavy cream (2/3 cup), stirring constantly until cheese is melted. Adjust seasoning to taste.
Remove the pot from the heat, then sprinkle top the pot with the remaining 1/2 cup jack cheese and 1 cup of cheddar. Cover pot with lid and let sit until cheese melts. Sprinkle with green onions and chopped tomatoes. Top as desired and Serve.