In a large skillet, melt 2 tablespoons butter over medium heat. Add onions and saute, stirring occasionally until onions are a deep brown and caramelized. (this will take about 15 minutes) Remove onions from pan and set aside.
Season chicken breasts on both sides with salt and pepper. Melt remaining tablespoon butter and olive oil in pan over medium-high heat. Sear chicken breasts on both sides until golden brown. Transfer to a plate.
Add both rices to skillet and saute at medium high about 2 minutes until golden. Add chicken broth and half and half to pan and add onions. Bring to a boil then nestle chicken breasts into pan and reduce heat to medium low and cover pan.
Let rice simmer 20-25 minutes over medium-low until most of liquid is evaporated, rice is fluffy, and chicken registers 165F. Sprinkle rice with parsley and Parmesan. Serve hot and enjoy!