Place your boneless, skinless chicken thighs in a large plastic ziplock bag and seal tightly. Use a meat cleaver to pound your chicken thighs until about ¼ inch thick. Season with salt and pepper.
Remove chicken thighs from bag. Pour flour into a shallow bowl. Dip the chicken thighs in the flour, coating each side in flour thoroughly.
Turn your Instant Pot on to the saute setting. Add 1 tbsp of butter and allow it to melt. Add the chicken thighs into the pot, browning them on each side (about 4 minutes each). Cook in two rounds if you need to so as not to crowd the chicken. Remove the browned chicken and set on a separate plate.
Still on the saute setting, add two more tablespoons of butter into your Instant Pot. Add the onions and mushrooms, and saute until the onions begin to turn translucent. Add small drizzles of olive oil if the bottom of the pot seems too dry.
Once the onions and mushrooms have softened, turn off the saute feature.
Pour the chicken stock and marsala wine into the Instant Pot, using a wooden spoon to scrape up any browned bits that had stuck to the bottom of the pot.
Add the chicken back into the pot, and put on the lid. Turn Instant Pot to Manual for 9 minutes. Once the 9 minutes are up, allow pressure to naturally release for 10 minutes, then instant release the rest.
Remove the cooked chicken from the pot and set on a separate plate.
Turn the Instant Pot to saute again, and allow the sauce to come to a boil.
In a separate bowl, combine cornstarch and water. Add into the boiling sauce, and stir until sauce thickens.
Serve chicken with sauce. Enjoy