01 -  In a small skillet set over medium-low heat, melt the butter. Add sliced onion, granulated sugar, and a pinch of salt. Cook gently, stirring occasionally, until the onions are deeply caramelized and golden, 12 to 15 minutes. Allow ample time to fully develop sweetness and complexity. 
 02 -  Transfer the caramelized onions and any pan juices to a blender. Add 2 tablespoons of milk; blend thoroughly until the mixture is completely smooth. Strain the purée through a fine-mesh sieve to achieve a silky consistency. 
 03 -  Brew 2 shots of espresso, then divide evenly between two cups. Into each cup, incorporate 1 tablespoon of the strained onion purée, stirring until well blended. 
 04 -  Heat the remaining milk until steaming, then froth using a milk frother or whisk until creamy and foamy. 
 05 -  Pour the frothed milk over the espresso-onion blends in each cup. Add honey or maple syrup if desired for a touch of sweetness. Gently stir and serve immediately, optionally garnishing with ground black pepper or fresh chive.