Brush goose with olive oil and sprinkle lightly with garlic powder, onion powder, salt, pepper and paprika. Roast in a 375°F degree oven for 20 minutes; reduce heat to 325°F and roast until juices run clear when inner thick is pierced with a cake tester or fork, or breast meat registers 155-160°F on a meat thermometer.
When goose is nearly done, prepare the sauce. Combine egg, milk and cornstarch, stirring to mix well.
In a saucepan, over medium high heat, melt butter and sauté green onions and mushrooms until onions are translucent. Stir in broth and bring to a boil. Reduce heat to a simmer.
Add cornstarch and milk mixture; simmer over very low heat, stirring occasionally until mixture thickens. Add lemon juice, salt and pepper, to taste and a pinch of paprika. Stir in wine and cook 10 more minutes.
Allow goose to stand at room temperature for 15 minutes before carving. Carve breast diagonally and arrange in a fan shape on plate. Pour sauce down the center. Garnish with parsley.
Serve accompanied by extra sauce for the table.
