Season chicken with salt and pepper. Heat 1 tablespoon garlic olive oil in a large frying pan over medium heat. Cook the chicken, turning once, until browned and just cooked through, about 7 to 10 minutes. Remove the chicken from the pan and put on a plate.
Add 1 tablespoon oil and mushrooms to the pan. Fry until they have released liquid and it has evaporated, about 4 minutes, stirring often.
Increase heat to high, add wine and cook until most of the wine has evaporated, about 4 minutes. Reduce heat to medium, stir in double cream and any accumulated juice from the chicken. Season to taste with salt and pepper. Return the chicken to the pan and turn so it is well coated with the sauce. Leave on low heat until thoroughly reheated. Sprinkle with parsley and serve with rice.