Preheat the oven broiler. Line a baking sheet with aluminum foil.
In a skillet over medium heat, cook the sunflower seeds 5 minutes, stirring constantly, until lightly toasted.
Place the pepper halves cut side down on the baking sheet. In a bowl, mix the olive oil, lime juice, balsamic vinegar, rosemary, salt, and pepper. Brush peppers with the olive oil mixture.
Roast peppers under the broiler 5 minutes, or until slightly charred. Remove from heat, peel, and slice. Toss with the toasted sunflower seeds to serve.