Heat olive oil and butter in a large stock pot. Add onion, garlic and crushed red pepper flakes and cook for 3 minutes. Add mushrooms and red pepper and cook until mushrooms are browned. Season with salt, pepper and paprika.
Add chicken breasts and pour in chicken stock. Bring to a boil, reduce heat to low and simmer for at least 45 minutes, until chicken is fully cooked. (This can simmer all day if you want.) Remove chicken and set aside.
Return soup to a boil and stir in rice. Remove heat and simmer until rice is tender, about 20 minutes. Meanwhile, shred or dice chicken.
After rice is cooked, stir chicken back into the pot. Add milk or cream and green onions. Season with additional salt and pepper, to taste.
Notes
Note – If you want your soup a little thicker, combine 1 tbsp. corn starch with 1/4 cup water. Bring the soup to a boil, stir in cornstarch mix and cook until thickened, about 5 minutes.