Turn the pressure cooker to saute setting. Heat the tablespoon of oil in the pressure cooker for 1-2 minutes.
Add carrots, celery, onion, garlic, potatoes, peas and mushrooms to the pot. Sautee for 3-4 minutes, stirring frequently.
Sprinkle the flour over top of the vegetable mixture and stir. Let the flour cook and soak into the vegetables for 2-3 minutes, stirring frequently.
Once the flour is cooked, and the vegetables mixture looks sticky in texture, add the seasonings, chicken broth, and chicken breasts. Stir the mixture so that everything is well combined.
Change the setting on the pressure cooker to HIGH pressure, ensure that the pressure valve is set to 'pressure' and set the timer for 20 minutes.
Once the timer goes off, let the pressure release naturally for 10 minutes. Release any additional pressure by carefully moving the pressure valve to 'release'.
Remove the chicken from the pot and shred. Add back to the pot and stir to combine.
Serve warm with biscuits or crusty bread and a side salad.