Rinse duck and pat dry. Cut off neck and wing tips, cut at the joint with a heavy kitchen knife.
Carve duck, cot with goose fat and season with salt and pepper. Rub with thyme and bay leaf, then cover and infuse for 12 hours in a cool place.
Add duck to a Dutch oven and bring to a boil. Cover and cook for 3 hours.
Duck may be chilled for up to 3 months.
Remove meat from bones and heat in an oven preheated to 200°C (approximately 350°F) for 10-15 minutes. Serve with fried potatoes, as desired.