Heat one tablespoon of olive oil in a skillet over medium heat. Add the diced onion, celery, and sliced mushrooms. Cook for approximately 8 to 10 minutes until softened, allowing the mushrooms to release their moisture. Stir in the garlic and cook for an additional minute. Once fragrant, transfer the vegetable mixture to the slow cooker insert.

In the same skillet, add the remaining tablespoon of olive oil and increase the heat to medium-high. Season the chicken breasts with salt and pepper before placing them in the skillet. Sear the chicken for about 3 to 4 minutes per side, or until browned. Once seared, turn off the heat and set the chicken aside.

Pour the chicken broth into the slow cooker, followed by the rice, lemon zest, lemon juice, Italian seasoning, and additional salt and pepper. Stir the mixture to combine evenly.

Add the seared chicken breasts, along with any juices accumulated in the skillet, into the slow cooker. Stir gently to ensure the chicken is evenly distributed.

Cover the slow cooker and cook on high for 4 hours. Begin checking the chicken for doneness after 2.5 to 3 hours, depending on the thickness of the chicken. If the chicken is fully cooked, remove it from the slow cooker, place it in a dish, and cover with foil to keep warm. Allow the rice to continue cooking until fully tender.

Once the rice is cooked, remove the lid of the slow cooker. Add the unsalted butter, frozen peas, and grated parmesan. Stir the mixture to incorporate the ingredients and heat the peas thoroughly.

Slice or chop the chicken and return it to the slow cooker, mixing it into the rice. Alternatively, serve the chicken on top of the rice mixture when plating.