01 - In a small saucepan over medium heat, melt the unsalted butter. Add the sliced onion and cook, stirring frequently, until deeply golden and caramelized, about 10 to 12 minutes.
02 - Add brown sugar and water to the pan with the onions. Simmer for 2 to 3 minutes, allowing the mixture to slightly thicken. Strain the syrup through a fine-mesh sieve, pressing to extract as much liquid as possible; discard solids. Let syrup cool.
03 - Prepare 2 shots (2 ounces) of espresso or brew strong coffee using your preferred method.
04 - Steam or heat the milk until frothy and hot. In each mug, pour 1 shot espresso and 1 to 1.5 tablespoons onion syrup. Add steamed milk, stir gently to combine, and adjust sweetness as needed.
05 - Fill a glass with ice cubes. Add 1 shot espresso and 1 to 1.5 tablespoons onion syrup, then top with cold milk. Stir well and serve immediately.