Roast the poblano peppers over an open flame, grill, or broiler until charred, about 10-15 minutes. Cover with plastic wrap and steam for 10 minutes.
Peel the charred skin off the peppers, cut a slit down each pepper, and remove the seeds.
Stuff each pepper with Monterey Jack cheese sticks, adding taco seasoning if desired.
Lay a tortilla flat, place a stuffed pepper on one edge, roll tightly, and secure with a toothpick. Repeat with remaining ingredients.
In a bowl, mix the beaten egg with 1 tablespoon of taco seasoning. Place cornmeal in another dish. Dip each flauta in egg mixture, then roll in cornmeal.
Heat canola oil in a skillet over medium heat. Fry flautas seam side down for 3-4 minutes per side until golden brown and crispy.
Transfer flautas to a paper towel-lined plate to drain excess oil. Squeeze lime over before serving.