Place a large pot over medium-high heat and add the olive oil. Once shimmering, add in the Italian sausage and sear, breaking up the meat until golden brown and fully cooked.
Remove the sausage from the pan and drain on paper towels. Set aside.
Reduce the heat to medium. If needed, add more olive oil, then add the chopped yellow onions and mushrooms (if using) with a pinch of salt. Cook until the onions are soft and translucent, around 5-7 minutes, then add in the minced garlic and cook for 1 minute more, being careful not to burn.
Stir in the tomato paste and cook for 1-2 more minutes, until sweetened, caramelized, and slightly darkened in color. Add the crushed tomatoes and red pepper flakes (if using), then carefully add the chicken stock and salt.
Once the soup boils, reduce the heat to a simmer and cook until thickened, around 15 minutes. Stir in the spinach (or kale), fresh tortellini, and heavy cream.
Cook for 3-5 minutes more, until the spinach is wilted and the pasta is tender. Remove the pot from the heat and serve warm with grated parmesan and French bread.