PLace the chicken along with the other ingredients and cover with water. Bring to a boil and cook until tender. Boneless chicken breast will cook in 12-15 minutes, bone in will take a little longer. Remove from heat when done and allow to cool so you can shred it.
Add the unpeeled potatoes to a pot of salted water and cook until tender. When done, remove from the heat and allow to cool. When you are able to handle, peel the potatoes.
Shred the chicken and add to a bowl. In another bowl, roughly mash the potatoes. Combine the chicken and the potatoes along with the grated muenster cheese. Salt and pepper to taste. Set aside
To assemble
Heat a skillet with a little oil. Heat to medium high and one at a time add the corn tortillas to soften and quickly remove them. Fill each tortilla with the chicken mixture until all are complete. Heat a skillet and fill with enough oil to fry the flautas. Heat to medium high and continually turn them to prevent burning. Drain on a wire rack or paper towels. To assemble:Spoon some of the Salsa verde onto the plate, Place 3 or 4 flautas on top. Ladle more sauce on top. Add shredded lettuce, Cotija cheese. Enjoy,Additional garnishes can be thinly sliced onions or pickled onions. Crema would be great. Guacamole or sour cream, yum.