Add 2 tablespoon of olive oil and 2 tablespoon of butter to the inner pot of the Ninja Foodi and turn the Sear/Sauté on high. Allow the butter and oil to heat up, but make sure it doesn't burn.
Slice the chicken breasts in half, lengthwise. You want the thickness to be about ½-1" thick and 4 pieces of chicken about the same size.
Combine the flour, salt, pepper, thyme in a bowl and spoon about a teaspoon onto each side of the chicken and rub it in. Or, you can remove a few Tablespoons of the flour mixture and dredge the chicken in it. Reserve the remaining flour flour for later.
Place the chicken breasts into the inner pot of the Ninja Foodi and let cook on high for 2 minutes. Flip and cook an additional 2 minutes. Remove from the pan and place into an 8" Fat Daddio Pan. Set aside.
Slice 1 pound of mushrooms and add to a sealable bag. Add remaining flour to the bag and shake to coat. Add 2 tablespoon of butter and 2 tablespoon olive oil and add in the mushrooms.
Saute for about 3-5 minutes or until you no longer see flour and the mushrooms have released their liquid. Add 1 cup of marsala wine and ½ cup of chicken stock.
Continue to cook on high on high sear/saute until the sauce begins to boil, then reduce the heat to medium. Simmer until the sauce thickens. This takes between 3-5 minutes. Stir frequently. When the sauce has thickened, pour it over the chicken in the Fat Daddio pan. Cover the pan with foil or a silicone cover. Wash the pot.
Peel and dice the potatoes into small dices. About 1-1½"dice. Add to the dry pot. Don't add the remaining chicken stock until you are ready to go under pressure.
Place frozen broccoli in a 6" Fat Daddio pan.
Pour the remaining ¾ cup of chicken stock into the inner pot. Place the covered pan on the rack in the low position. Place the pan with the broccoli on top, uncovered.
Put the pressure lid on and turn the valve to seal. Set the pressure to high for 2 minutes. When the time is up, immediately release the pressure.
Remove the pan with the broccoli and cover to keep hot. Remove the pan with the chicken and keep covered. Remove the rack and set aside. If the potatoes have a lot of liquid, turn the sear/sauté on and burn most of it off before adding cream and butter.
Add 2 tablespoon of cream and remaining 1 tablespoon of butter to the potatoes and mash with a hand masher that is safe for the non-stick pot. Add additional 1 tablespoon of cream and 1 tablespoon of butter if needed. Season to taste.