Bring a large pot of salted water to a boil.
Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Squeeze the sausage meat out of the casings into the pan. Break it apart with a wooden spoon and cook until browned and cooked through. Remove the meat and set aside, leaving the fat in the pan.
Add the sliced mushrooms and diced onion to the hot sausage fat. Cook for about 5–7 minutes until the mushrooms are browned and the onions are soft.
Reduce heat to medium. Stir in the garlic flower paste and cook for just 30–60 seconds. You want it to become fragrant and melt into the vegetables, but be careful not to burn it. (If using dried herbs like oregano, add them now too).
Pour in the tomato sauce and scrape the bottom of the pan to lift up the flavorful browned bits. Add the cooked sausage back into the pan. Let this simmer on low heat for 10 minutes to thicken slightly.
While the sauce simmers, boil the tortellini. Cook them for 1 minute less than the package instructions. Reserve ½ cup of pasta water, then drain.
Add the tortellini directly into the skillet with the sauce. Toss gently to coat. If the sauce is too thick, add a small splash of the reserved pasta water. Top immediately with your grated cheese and serve.