Pat chicken thighs dry with paper towels and season well on both sides with salt and pepper.
Heat a 4-qt instant pot using BROWN/SAUTE function. Add butter and olive oil to instant pot and swirl to evenly coat bottom. Add chicken thighs to instant pot and sear 3-4 minutes on each side until a deep golden brown. Transfer to a plate and set aside.
Add pepper, onion, and mushrooms to drippings in instant pot and saute 3-5 minutes until tender. Add garlic and saute 1 additional minute until fragrant. Add red wine and cook until reduced in half. Turn off instant pot.
Add crushed tomatoes, bay leaf, oregano, and thyme to instant pot and stir until combined. Arrange chicken thighs in instant pot.
Seal lid onto instant pot and set vent to closed. Cook chicken on high pressure 15 minutes, then turn off instant pot and let release pressure naturally for 15 minutes.
Release any remaining pressure from instant pot and remove lid. Remove bay leaf and thyme from instant pot and discard. Remove chicken thighs and use a fork to pull chicken from the bone and shred. Discard bones and skin.
Add chicken back to instant pot and season sauce with salt and pepper to taste if needed. Top cacciatore with fresh basil and serve over cooked pasta or polenta warm. Enjoy!