Heat the oven to 392°F (200 °C). Chop the onion, garlic and thyme and put them on the bottom of a large baking tray. Put the two ducks on top. Pierce their skins with a fork or sharp knife and season them with salt and pepper.
In a pot, pour in the beer and sugar and allow the mixture to boil. Once the sugar is completely melted, remove it from the heat and pour the liquid over the ducks. Bake for about 2 hours, until browned and the legs come off easily.
During baking, occasionally open the oven and top the meat with the juice from the tray. When the ducks are ready, remove them from the tray and allow them to rest in a warm area. Drain the excess fat from the tray and pour in the broth to it.
Allow the liquid to boil and leave it on the stove for about 10 minutes. Season with salt and pepper, strain and serve the birds with the sauce.