For balsamic onion glaze, heat oil in a large sauté pan over medium heat and add onions. Sweat onions, stirring often, until all liquid had evaporated, about 20 minutes, Add half of balsamic vinegar and simmer until absorbed. Add remaining balsamic and reduce until a glaze. Season to taste and set aside.
For salmon, preheat a grill to medium-high. Reduce balsamic with rosemary in a small saucepot until a glaze, about 8 minutes and set aside. Brush salmon fillets lightly with olive oil and season. Grill, skin-side up, for 4 minutes, then rotate 90 degrees and cook 4 more minutes. Turn salmon over and cook for 8 more minutes for medium doneness. Brush salmon with balsamic during last 5 minutes of cooking.
Serve salmon with Balsamic Onions on the side.
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