Set pressure cooker to "sear", adjust time to 15 minutes, and add oil. Add sausage and cook until brown. Remove sausage and set aside on paper towel to drain. Retain fat in cooker.
Add onion and sauté until translucent. Add garlic and sauté for an additional 2 minutes.
Deglaze pot with red wine, making sure to scrape bottom of pot to release fond. Allow liquid to simmer until reduced by half.
Add tomatoes with juice, chicken stock, balsamic vinegar, brown sugar, Parmesan rind (optional), sausage, and tortellini.
Close and lock lid. Set pressure cooker to "soup" and adjust time to 5 minutes.
When done, quick release and make sure all pressure is released before opening lid.
Carefully open lid and add spinach. Check seasoning and add salt and pepper, if needed.
Ladle into serving bowls and top with a drizzle of extra-virgin olive oil and shaved Parmesan.
