1. Preheat barbecue to 350 degrees for indirect heating.
2. Place leak pieces in large bowl. Add onions, carrots, salt, pepper, mushrooms, sugar and oregano. Stir well.
3. In a cast-iron skillet over high heat, brown goose breasts in olive oil, until meat is seared on all sides. Set aside.
4. Pour vegetables over goose in skillet. Add half-and-half and stir well.
5. Cover top of skillet with pie crust, folding the edges under. Cut a few small vents in the crust.
6. Place over indirect heat on barbecue grill, cover, and cook for approximately 1 hour.
7. Remove from barbecue and serve directly from the skillet.