Preheat the broiler. Line a baking sheet with foil.
Put the poblano skin-side up on the prepared baking sheet and broil until the skin is wrinkled and charred in spots, 2 to 3 minutes. Transfer the poblano to a small bowl, cover with plastic wrap and let steam for 5 minutes. Run the poblano under cold water and remove and discard the skin. Cut the poblano into very small pieces and return to the bowl.
Toss the chicken with the oil, chili powder and 3/4 teaspoon salt in a medium bowl. Transfer to the baking sheet and broil, turning once, until browned in spots and cooked through, 4 to 5 minutes per side. Let cool for a few minutes, cut into chunks and transfer to a food processor. Add 1 cup of the cheese, half of the scallions and 1/4 teaspoon salt; pulse until the mixture is coarse and holds together when squeezed.
Melt the butter in a small saucepan over medium heat. Add the flour and stir until the mixture is light brown, about 45 seconds. Whisk in the milk and cook, whisking until the mixture begins to bubble and thicken, about 4 minutes. Whisk in the remaining 1 cup cheese. Stir in the chopped poblanos, hot sauce, garlic and 3/4 teaspoon salt. Set aside and keep warm.
Wrap the tortillas in a damp cloth and heat in the microwave for 1 minute so they are warm and pliable. Lay the tortillas out and spread 1/4 cup of the filling in the middle of each. Roll each up and secure with a toothpick. Push the filling into the ends a little so that it doesn't fall out.
Heat about 1/4 inch of oil in a large skillet over medium heat. Once the oil is shimmering and hot, add half the taquitos and fry, turning as needed, until golden brown on all sides, about 4 minutes. Transfer to a paper-towel-lined plate and sprinkle with salt. Repeat with the remaining taquitos.
Remove the toothpicks and arrange the taquitos on a serving platter. Drizzle with some of the cheese sauce and top with the remaining scallions.
Copyright 2015 Television Food Network, G.P. All rights reserved.