Preheat the oven to 400ºF. Line a baking sheet with foil and place a baking rack on top. Spray with nonstick cooking spray.
In a large bowl, mix the Monterey Jack cheese and the cream cheese together until blended. Add the shredded beef, green chiles and cilantro and stir to combine.
Heat the tortillas in the microwave for 30 seconds to soften them. Spread some of the beef mixture on the lower third of the tortilla, staying a little bit away from the edges. Roll the tortilla, then place on the baking rack, seam side down. Repeat with the remaining tortillas and filling.
Spray the rolled taquitos with nonstick cooking spray, then sprinkle with coarse salt. Bake in the preheated oven until browned and crisp, about 10 minutes. Remove from the oven and allow the taquitos to cool slightly before serving.