In a Dutch oven, melt butter over medium-low heat. Add onion; cover and cook for 30 minutes, stirring occasionally. Remove cover and increase heat to medium-high. Stir onion frequently until golden brown, 10 to 12 minutes. Add vinegar, salt and pepper; stir until vinegar evaporates, 1 to 2 minutes; set aside.
In a large skillet, heat olive oil over medium-high heat. Add chicken, Italian seasoning and garlic salt. Cook, stirring frequently, for 12 minutes or until chicken is lightly browned; set aside.
Preheat oven to 425 deg. Line two baking sheets with aluminum foil.
Slice each bagel in half horizontally. Spread Boursin cheese on each bagel half. Top each bagel half with pesto, chicken and caramelized onions. Sprinkle with Parmesan cheese. Place on prepared pan; bake for 10 minutes or until cheese is melted.
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Italian Chicken and Caramelized Onion Bagel Pizzas (cont.)