Place salmon in a shallow glass dish. In a small bowl, whisk together olive oil, balsamic vinegar, brown sugar, soy sauce, garlic and salt and pepper, to taste. Cover and refrigerate for at least one hour.
Meanwhile, preheat the grill for medium-high heat. Place the blackberries in a medium bowl. Brush the bell pepper halves, jalapeno pepper and onion slices with olive oil. Season with salt and pepper.
Grill until vegetables are charred, about 10 minutes, turning once halfway through cooking time. Cool completely, then dice peppers and onions. Add vegetables to the bowl with the blackberries.
Stir in blackberry jam, honey, lime juice and mint, and toss gently to mix well. Refrigerate until ready to serve.
To cook the salmon, oil grill and preheat for medium heat. Cook for 10-12 minutes, or until internal temperature reaches 145 degrees, turning once halfway through cooking.
Transfer salmon to a serving platter and top with blackberry bell pepper salsa.