In a large pan set over medium heat, add the butter and chicken cubes and cook, approximately 30 seconds each side. Add the onions, carrots, and mushrooms and cook 3-4 minutes, stirring often. Season.
Stir in the flour and continue to cook another minute. Add the broth, stir, and cook until broth has thickened (4-5 minutes). Add the milk, reduce heat to low and continue to cook 5 minutes. Add the green peas and continue to cook 2 minutes.
On a clean work surface, cut off 1/3 of each pocket and open them. Place half a cheese slice in each pocket (fold the slices over so that they remain on top of each pocket).
Fill each pocket with the chicken mixture.
Place the pockets on a baking sheet lined with parchment paper, cheese side up, and heat under the broiler for approximately 30 seconds (keep an eye on them). Serve.