Heat olive oil in a large skillet over medium-high heat. Sear the chicken breasts for 3-4 minutes per side until golden brown but not cooked through—this step locks in juices and builds deeper flavor.
Layer the slow cooker by adding diced onion and minced garlic to the bottom. Pour chicken broth over the aromatics, then nestle the seared chicken breasts on top without crowding.
Cook on the low setting for 4 hours, then carefully remove chicken breasts and shred them using two forks. Return shredded chicken to the pot—this texture distribution ensures every bite contains meat rather than creating chunks.
Add uncooked rice, sliced mushrooms, diced carrots, dried thyme, rosemary, salt, and pepper. Stir gently to combine, then cook on low for exactly 2 more hours until rice reaches tender but not mushy consistency and the slow cooker chicken and rice mixture achieves creamy cohesion.
In the final 10 minutes, stir in frozen peas and let them thaw naturally from residual heat. This preserves their bright color and prevents mushiness compared to adding them earlier.
Remove from heat and stir in heavy cream and butter until fully incorporated. Taste and adjust seasonings—salt and pepper often need slight correction after the long cook. Garnish with fresh parsley and serve immediately while steam carries the aromatics upward.