Turn a 6 quart or larger Instant Pot to saute setting. Add the olive oil, onion and carrots. Saute, stirring, until the vegetables start to soften, 3-5 minutes.
Stir in the garlic, brown rice, Dijon mustard, Italian seasoning, garlic powder, salt and pepper. Cook for 1 minute, stirring. Turn off Instant Pot.
Add the chicken broth and stir until well combined, making sure to scrape 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. Do not stir.
Place the lid on the Instant Pot and set the pressure valve to sealing. Pressure cook on high for 20 minutes.
Allow the Instant Pot to naturally release for 12 minutes (by leaving it off after it finishes cooking).
Then, carefully do a quick pressure release (use the handle of a long spoon to carefully turn the valve to venting) to release the remaining steam and pressure. Once the float valve drops down, carefully open the Instant Pot away from you, as the steam will be hot.
Remove the chicken to a cutting board and chop into bite-size pieces. Stir the chicken back into the rice mixture, along with the peas.
Serve with fresh parsley and grated Parmesan, if desired.