Preheat the oven to 400°F (200°C).
Line a large baking sheet with the tortilla chips in a mostly single layer, allowing some overlap if needed.
Sprinkle 1 cup of the shredded Monterey Jack evenly over the chips.
Scatter the shredded rotisserie chicken, rinsed white beans, and green chiles over the cheese layer.
Top with the remaining 1 cup of cheese to cover the toppings.
Bake in the preheated oven until the cheese is melted and bubbly, about 5 to 7 minutes.
Remove from the oven and immediately top with cubed avocado, sliced scallions, chopped cilantro, sliced jalapeño, and dollops of sour cream.
Spoon salsa verde over the nachos or serve it on the side, then serve immediately.