Prepare the Rabbit: Begin by patting the rabbit pieces dry with paper towels. Season generously with salt and pepper.
Sauté the Rabbit: Set your Instant Pot to the 'Sauté' function and heat the olive oil. Once hot, add the rabbit pieces in batches and brown on all sides, about 3 minutes per side. Transfer to a plate and set aside.
Cook the Vegetables: In the same pot, add the onion, garlic, celery, and carrots (or low-carb substitute). Sauté until the onions are translucent and the vegetables begin to soften, about 5 minutes.
Deglaze the Pot: Pour in a splash of chicken broth and use a wooden spoon to scrape up any browned bits from the bottom of the pot — this will add flavor to your stew.
Combine Ingredients: Return the rabbit to the pot along with turnips, thyme, rosemary, bay leaves, and remaining chicken broth. Stir to combine.
Pressure Cook: Seal the Instant Pot lid and set to 'Manual' or 'Pressure Cook' on high for 30 minutes. After cooking, let the pressure release naturally for 10 minutes, then quick-release any remaining pressure.
Final Seasoning: Carefully remove the lid and discard the bay leaves. Taste for seasoning and adjust with salt and pepper as needed.
Serve: Ladle the stew into bowls and garnish with fresh parsley.