Heat a medium saucepan over medium heat, add the butter and allow to melt. Add the flour, whisking to combine. Let the roux cook for a minute until a pale golden brown. Add the milk, whisking to incorporate.
Bring the mixture to a simmer, then lower the heat to medium-low, whisking until the sauce thickens, about 2 minutes. Slowly add 1 cup of the cheddar, the Monterey Jack cheese and salt, whisking to combine, until the cheese is completely melted.
Preheat oven to broil, high. Spread the chips on a baking sheet and ladle cheese sauce over the top. Spread the remaining Cheddar cheese over the top and broil until the Cheddar has melted, about 1 minute. Remove from the oven and spread the chips topped with cheese on a large platter.
Top with the grilled chicken, beans, green onions, queso fresco, pico de gallo, avocado, jalapeños and sour cream.