Pour condensed milk into a 9-inch deep-dish pie plate and cover with foil. Put pie plate in a roasting pan and add enough hot water to pan to reach halfway up side of pie plate. Bake milk in middle of oven until thick and golden, about 1 1/2 hours. Check about halfway through cooking time and add more water if necessary to the roasting pan. Carefully remove pie plate from pan and cool completely.
Add remaining ingredients to milk and whisk until smooth. Sauce may be made 2 days ahead and chilled, covered.