Preheat the oven to 400°F (200°C).
Prepare the toppings: peel, seed, and cube the avocado; slice the green ends of the 2 scallions thinly; chop the 1/2 cup cilantro; seed and thinly slice the jalapeño; have the 1/2 cup sour cream and salsa verde ready to serve.
Arrange the 15 oz tortilla chips on a large rimmed baking sheet in mostly one layer (a little overlap is fine).
Sprinkle 1 cup of the shredded Monterey Jack cheese evenly over the chips.
Evenly distribute the 2 cups shredded rotisserie (or cooked shredded) chicken, the 15 ounces white beans (rinsed and drained), and the 4 ounces green chiles over the cheese-covered chips.
Sprinkle the remaining 1 cup of shredded cheese evenly over the toppings.
Bake in the preheated oven until the cheese is melted and bubbling, about 5 to 7 minutes—check at 5 minutes to avoid overbrowning.
Remove the baking sheet from the oven and immediately top the nachos with the cubed avocado, sliced scallions, chopped cilantro, and sliced jalapeño.
Dollop or spoon the 1/2 cup sour cream over the nachos, then spoon salsa verde over the top or serve the salsa on the side.
Serve the nachos immediately.