Turn Instant Pot on saute setting. Add the olive oil and onion and cook 2 minutes, until onion starts to soften. Add the ground turkey and cook, stirring to crumble the meat, until turkey is cooked through, about 5 minutes. Turn off the Instant Pot and stir in the garlic.
Add the brown sugar, chili powder, cumin, oregano, salt, pepper and tomato paste. Stir to combine. Add the broth and stir well, scraping up any bits from the bottom of the pot.
Add the crushed tomatoes and then beans on top of the meat mixture and DO NOT stir in.
Seal the Instant Pot lid and turn the valve to sealing. Pressure cook on high pressure (manual) for 12 minutes.
Allow the Instant Pot to naturally release for 10 minutes (by leaving it off after it finishes cooking). Then, carefully do a quick pressure release (use a potholder or the handle of a long spoon to carefully turn the steam release valve to venting) to release the remaining steam and pressure. Once the float valve drops down, carefully open the Instant Pot away from you, as the steam will be hot.
Stir and serve chili with toppings, as desired.