Heat the oil in a skillet over medium-high heat and brown the sausage into bite-size crumbles, 7 minutes.
Add the onion and cook for 4 minutes, then stir in the garlic for 30 seconds.
Transfer the mixture to a 6-quart slow cooker and add the marinara, broth, oregano and pepper.
Cover and cook on low for 4 1/2 to 5 hours until the sauce tastes integrated.
Switch the cooker to high, stir in the tortellini and cover until the pasta is tender at the pinched edge, 20 to 30 minutes.
Fold in the spinach by handfuls and cover for 3 minutes until wilted.
Serve immediately with Parmesan, before the tortellini softens further.