Preheat the oven to 375 degrees F. Bring a large pot of salted water to a boil. Add the green beans and cook until crisp-tender, about 6 minutes. Drain, rinse under cold water and blot dry with paper towels.
Melt the butter in a large pot or Dutch oven over medium heat. Add the poblanos and onion, season with salt and cook, stirring occasionally, until tender, about 7 minutes. Add the garlic and cook 1 minute. Add the flour and cook, stirring, until the vegetables are coated, about 1 minute.
Whisk in the half-and-half, chicken broth, cayenne and 1/2 teaspoon salt. Increase the heat to medium high and bring to a boil, then reduce the heat to medium low and simmer, whisking occasionally, until thickened, about 5 minutes. Add the pepper jack and stir until melted, then add the green beans and stir to coat. Transfer to a 3-quart baking dish. (You can refrigerate the casserole, covered, for up to 4 hours.)
Bake the casserole until bubbling, about 20 minutes. Meanwhile, pulse the tortilla chips with the chile powder in a food processor until coarsely ground. Sprinkle the Cotija cheese and ground tortilla chips over the casserole; bake until golden, about 5 more minutes.