Start by heating the olive oil in a skillet over medium heat. Season the boneless skinless chicken breasts with sea salt and pepper. Add the chicken to the skillet and cook for about 6-8 minutes on each side, or until fully cooked. Once done, remove from heat and allow to cool slightly before slicing into bite-sized pieces.
In the same skillet, create a white roux. Melt 2 tablespoons of butter over medium heat, then whisk in 2 tablespoons of all-purpose flour. Cook for about 2 minutes, stirring constantly until it turns a light golden color. Gradually whisk in 4 cups of whole milk, continuing to stir until the mixture thickens. Add in 4 ounces of shredded asiago cheese and stir until melted and smooth.
Preheat your oven to 375°F (190°C). In an oven-safe dish, spread a layer of corn tortilla chips across the bottom. Top with a generous amount of the shredded mozzarella cheese, diced tomatoes, sliced black olives, kalamata olives, banana peppers, and the sliced chicken.
Drizzle the creamy asiago cheese sauce over the layered nachos, making sure to cover as much as possible. Add more toppings if desired, including extra cheese and veggies.
Place the dish in the preheated oven and bake for approximately 15-20 minutes, or until the cheese is bubbly and slightly golden.
Once baked, remove from the oven and sprinkle the sliced green onions on top for a fresh finish. Serve immediately with additional toppings on the side, such as guacamole or sour cream if desired.