01 - In a small skillet set over medium-low heat, melt the butter. Add the sliced onion, granulated sugar, and a pinch of salt. Sauté gently, stirring occasionally, until onions are deeply caramelized and golden brown, approximately 12 to 15 minutes. Maintain low heat to develop rich flavor without burning.
02 - Transfer the caramelized onions along with all pan juices into a blender. Add 2 tablespoons of milk. Blend until the mixture is completely smooth, then strain through a fine-mesh sieve to achieve a silky consistency.
03 - Brew 2 shots (2 fluid ounces) of espresso and pour evenly into two cups. Add 1 tablespoon of strained onion purée to each serving and stir to combine thoroughly.
04 - Heat the remaining milk until it begins to steam. Froth using a milk frother or vigorously whisk until creamy and foamy.
05 - Pour the foamed milk over the espresso-onion mixture in each cup. Sweeten to taste with honey or maple syrup as desired. Stir gently and serve immediately.