Toss together grated Monterey Jack cheese, 2 ½ ounces blue cheese crumbles, and cornstarch in a large bowl with gloved hands until cheese is evenly coated. Set aside until ready to use.
Combine unsalted butter and water in Dutch oven1, then bring it to a simmer. Add the salt and penne. Cook, stirring often to keep the pasta from sticking, until about ⅔ of the water has been absorbed and pasta is very al dente, about 6-8 minutes (about 2 minutes minus al dente on package directions).
Add Frank's buffalo wing sauce and freshly ground black pepper to pasta and cook, stirring often, until about half of the sauce has been absorbed and the pasta is al dente, about 2 minutes.
Reduce the heat to low and add the reserved cheese mixture a handful at a time, stirring after each addition until the cheese is mostly melted before adding more. Stir until all of the cheese is melted and the mixture is creamy. Stir in the shredded chicken. Remove from the heat. Taste the pasta, adjust the seasonings, and add more buffalo sauce if needed.
Top with remaining blue cheese crumbles and thinly sliced green onions.