If using meat: heat 1 tbsp olive oil in a large skillet over medium heat and brown the ground beef and hot sausage until no pink remains; drain excess fat. For vegetarian/vegan version: skip browning meat and proceed to the next step.
In the bottom of a large sauce pot, heat 1 tbsp olive oil over medium heat (or reuse the skillet fat if not vegetarian). Add the chopped onion, minced garlic, and sliced mushrooms and cook until the onion is softened and mushrooms are browned, about 5–7 minutes.
If using shredded MorningStar Farms patties for the vegetarian version, add them now to the pot and stir to combine.
Add the crushed tomatoes, tomato paste, sugar, cumin, oregano, and the browned meat (if using) to the pot. Stir until the tomato paste is fully incorporated.
Bring the sauce to a gentle boil, then reduce heat to low and simmer. Season with salt and pepper to taste.
Simmer until flavors meld and sauce reaches desired thickness, about 20–30 minutes; add water as needed to adjust consistency. The longer it simmers, the richer the flavor.