Grate both the pepper jack and Cheddar cheese and toss with the cornstarch in a bowl. Set aside.
Heat a large saucepan over medium heat and add the butter. When melted, add the squash, chipotle powder and salt and saute until the squash caramelizes a bit, about 5 minutes. Add 1 cup water, cover, bring to a simmer and simmer until very tender, another 10 minutes. Remove from the heat, add the milk and use an immersion blender to blend until silky and smooth. Add the cheese mixture, return to the heat and cook, whisking, until the cheese melts. Season with additional salt as needed.
Serve with tortilla chips and garnish with scallions and banana peppers.