1Heat 1 tablespoon of olive oil in a medium saucepan over medium heat. Add garlic and saute for 5 minutes. Remove from heat and stir the garlic mixture into the red wine vinegar. Place the goose breasts into a shallow glass dish and cover with the vinegar mixture. Cover and refrigerate for at least 4 hours.
2In a medium saucepan over medium heat, combine the milk, onion and carrot. Gradually bring to a boil, stirring frequently. Season with pepper to taste. As soon as the mixture comes to a boil, remove from heat, cover and set aside.
3Preheat oven to 350 degrees F (175 degrees C). Place goose breasts and marinade into a baking dish and cover with foil.
4Roast for 25 to 30 minutes in the preheated oven. Cook white rice according to package directions. Heat two tablespoons of oil in a small saucepan over medium-low heat. Add mushrooms and saute for 5 minutes. Whisk in the flour, stirring for 2 minutes, then gradually whisk in the milk mixture. Season with rosemary, salt and pepper. Bring to a boil, stirring constantly, then reduce heat to low and simmer for 3 minutes.
5Make a bed of cooked white rice on a serving platter. Lay the goose breasts on top and pour the sauce over all.