Heat the olive oil in a large, deep skillet over medium-high heat. Season the chicken pieces with salt and pepper. Add the chicken to the skillet and cook until browned on all sides, about 5-7 minutes. Remove the chicken and set it aside.
Add the sliced mushrooms to the same skillet and cook until they release their liquid and start to brown, about 5 minutes.
Add the chopped onion and cook until softened, about 3 minutes. Add the minced garlic and dried thyme; cook for 1 minute until fragrant.
Pour in the chicken broth and scrape up any browned bits from the bottom of the skillet. Add the uncooked rice, stir once, and bring the mixture to a simmer.
Reduce the heat to low, cover the skillet, and cook for 15 minutes, or until the rice has absorbed most of the liquid. Do not stir during this time.
Return the cooked chicken to the skillet. Stir in the heavy cream and Parmesan cheese. Cook uncovered for 2-3 minutes, stirring gently until the sauce thickens slightly and the chicken is heated through.
Remove from heat. Garnish with fresh parsley before serving directly from the skillet.
Notes
For a richer flavor, use a mix of mushroom varieties like shiitake or oyster mushrooms.
If the sauce seems too thick, stir in a splash of extra chicken broth or milk until you reach your desired consistency.
Do not lift the lid while the rice is cooking in step 4; this traps the steam needed to cook the rice properly.