01 - Heat olive oil and 2 tablespoons of butter in a large skillet over medium heat until melted and slightly foamy.
02 - Add sliced onions and sea salt. Cook, stirring occasionally, until onions soften and begin to caramelize, about 20 to 25 minutes.
03 - Reduce heat to low. Stir in brown sugar and cook for another 5 minutes until onions turn golden and jammy.
04 - In a small saucepan, melt the remaining 1 tablespoon butter over medium heat until it foams and turns golden brown with a nutty aroma, about 2 to 3 minutes. Remove from heat.
05 - Add balsamic vinegar to the onions, stirring to deglaze the pan and coat the onions evenly. Cook 2 to 3 minutes until vinegar has mostly evaporated and glaze thickens.
06 - Drizzle the browned butter over the glazed onions, season with black pepper, stir to combine, and serve warm.