In a large skillet, heat oil over medium-low heat. Add the onions, and cook, stirring occasionally, until golden-brown, about 15-20 minutes. Season with salt and pepper. Set aside.
Meanwhile, preheat oven to 375°F and line a rimmed baking sheet with parchment paper. Cut the top-third off of the Tribeca Oven Ciabatta Loaf. Carefully hollow out the bottom, leaving a 1-inch shell of bread intact for support. Slice top of loaf into 1/2-inch-thick pieces to create crostini. Set hollowed-out loaf aside.
Place the bread pieces on the prepared baking sheet and drizzle with 1 tablespoon of oil. Bake, flipping crostini halfway through, until golden-brown and crisp, about 10-15 minutes. Set aside for serving with dip.
Increase oven temperature to 400°F. In a food processor, combine the cream cheese, cheddar, Monterey Jack cheese and onions, and pulse until just combined. Spoon the cheese mixture into the hollowed out loaf. Transfer to a parchment-paper-lined rimmed baking sheet. Bake until the cheese is melted and light golden-brown, about 7-10 minutes. Top with chives. Serve with crostini and pepperoncini.