Preheat oven to 375 degrees.
In a large oven proof skillet, add olive oil over a medium heat.
Saute onions, mushrooms and thyme until the onions are translucent; about 5 minutes.
Season with salt and pepper.
Remove from heat and add to a bowl.
Scoop a few tablespoons of the mushroom mixture and place in the middle of the chicken. Sprinkle goat cheese.
Roll the chicken and secure with toothpicks. Repeat with other chicken breasts.
Season chicken with salt and pepper.
Place rolled chicken in the same skillet used for the mushroom mixture.
Bake for 35-40 minutes, or until the internal temperature of the chicken is 165 degrees.
Remove chicken from skillet; cover with foil to keep warm.
In the same skillet, add butter and flour.
Stir constantly until the color of the flour is light brown.
In a steady stream, pour in warmed chicken stock and wine.
Stir until the sauce starts to thicken.
Let it simmer for 5 minutes.
Remove from heat and add parsley.
Drizzle over chicken when serving.
Microwave rice according to directions.
Add cooked rice to the bowl of the leftover mushroom filling.
Stir in parsley.
Serve with chicken and pan sauce.