Set the Instant Pot to the saute function. Add onions, carrots and olive oil and cook until soft, about 5 minutes. Add mushrooms and cook for an additional 1-2 minutes.
Carefully add the ground turkey to the pot and stir. Season with salt, pepper, garlic powder, thyme, and red pepper flakes. Cook until no longer pink.
Turn off the Saute function and pour in the tomato sauce and beef broth. Close the lid and Pressure Cook for 15 minutes.
Quick release the Instant Pot and add in the cabbage. Cook for an additional 5 minutes and then quick release.
Stir in cooked rice, top with green onions, and serve right away.
Notes
To make this on the stovetop, repeat the steps above but instead of pressure cooking, simmer over medium heat with a lid for the same amount of time.