Heat 1 tablespoon olive oil in a large skillet over medium heat.
If using meat: add ground beef and hot sausage and brown, breaking up with a spoon, until no pink remains; drain excess fat if needed.
If making the vegetarian version: skip browning meat and proceed to the next step to cook the vegetables in oil.
Add the chopped onion, minced garlic, and sliced mushrooms to the pot or skillet and cook until the onion is translucent and mushrooms are softened, about 5–7 minutes.
Transfer the browned meat and vegetables to a large sauce pot (or if you browned meat in the pot, keep them there).
Add the crushed tomatoes, tomato paste, sugar, cumin, oregano, and salt and pepper to taste; stir to combine.
Bring the sauce to a boil, then reduce heat to low and simmer until heated through and flavors meld, at least 20–30 minutes; add water as needed to reach desired thickness.
For the vegetarian/vegan option: shred the MorningStar Farms sausage patties and stir them into the simmering sauce until heated through.
Taste and adjust seasoning, then serve over cooked pasta.