01 - Combine ube halaya, water, and condensed milk in a small saucepan over low heat. Stir continuously until smooth and warmed through, about 2-3 minutes. Remove from heat and whisk in vanilla extract until fully incorporated.
02 - For hot latte: Steam or heat milk until frothy but not boiling. For iced latte: Use cold milk and prepare serving glasses with ice cubes.
03 - Divide the warmed ube mixture evenly between two serving mugs or glasses, spreading along the bottom.
04 - Pour one shot of espresso (or 1 fluid ounce strong coffee) into each glass over the ube base.
05 - Slowly pour the steamed or cold milk over the espresso and ube mixture. Stir thoroughly to blend flavors and achieve a uniform purple color throughout.
06 - Top with whipped cream and a light dusting of ube powder or yam flakes if desired. Serve immediately while hot or over ice.