Heat the olive oil in a 6 quart or larger Instant Pot using the saute setting. Add the onion and carrots. Saute, stirring, until the vegetables start to soften, about 3 minutes. Turn off the Instant Pot.
Stir in the garlic. Add the brown rice, Dijon mustard, Italian seasoning, garlic powder, salt, pepper and chicken broth. Stir well, scraping up any bits that are stuck to the bottom of the pot.
Make sure that all of the rice and vegetables are in the liquid, not on the sides of the pot. Place the chicken breasts on top of the rice mixture.
Close the Instant Pot lid and set the pressure valve to sealing. Pressure cook on high pressure for 20 minutes. The Instant Pot will take about 15 minutes to come to pressure and then the cook time will begin counting down.
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 by moving the steam release valve to the venting position. Once all of the steam has been released and the pin drops down, carefully open the Instant Pot lid.
Remove the chicken to a cutting board. Stir the peas into the Instant Pot, close the lid, and let sit for 5 minutes to heat the peas through.
Cut the chicken into bite-size pieces. Stir the chicken back into the rice mixture in the pot.
Serve with fresh parsley and grated Parmesan, if desired.