Put the flour mixture on a large plate. Dredge (coat) the chicken cutlets in the flour mixture on both sides so they’re fully and lightly dusted.
Add the olive oil to the Instant Pot, hit Sauté, and Adjust to the More or High setting. After 3 minutes of heating, add the chicken in batches and sear on each side for 1 minute, until lightly browned. Use tongs to transfer the seared chicken to a plate to rest. Repeat until all the chicken is seared.
Add the butter to the pot. Once melted, add the mushrooms and sauté, stirring often, for about 3 minutes, until softened and cooked down.
Add the broth and return the chicken to the pot, resting the cutlets on top of the mushrooms and broth in a crisscross fashion. Top with the spinach. Secure the lid and move the valve to the sealing position. Hit Cancel and then hit Pressure Cook or Manual on High Pressure for 5 minutes. Quick release when done.
Use tongs to transfer the chicken to a serving dish. Hit Cancel and then hit Sauté and Adjust so it’s on the More or High setting. Once it begins to bubble, stir in the cream cheese, pesto, Parmesan, and frozen peas (if using). Don’t worry about them being frozen. The heat of the sauce will thaw them immediately. Once the cream cheese is melded into the sauce, hit Cancel to turn the pot off.
Drape the sauce over the chicken in the serving dish and top with crumbled feta (if using).