Combine the browned flour with ½ cup of the liquid from the Roast Leg of Lamb and set aside.
Place the remaining liquid from the roast, the beef stock, and the mint leaves into a heavy 3-quart pot over high heat. Bring to a full boil, whisk in the flour/stock mixture, reduce the heat to medium, and simmer for 5 minutes. Remove from the heat and add the artificial sweetener.