Pre-heat barbecue to 350 F for indirect heating.
Cut leaks and place in large bowl, add diced onions, carrots, salt and pepper, quartered mushrooms, sugar, and oregano and stir well.
In cast iron skillet over high heat, brown the goose breast cubes in olive oil, until meat is seared on all sides, set aside.
Pour vegetables into the skillet, add the half and half and stir well.
Cover top of the skillet with a pie crust, folding the edges under, making sure to put several small vents in the crust.
Place over indirect heat on barbecue grill, cover, and cook for approximately 1 hour.
Remove from barbecue and serve on the table directly from the skillet.