Cook the beef: Brown the ground beef in a large skillet over medium heat, breaking it apart as it cooks. Drain any excess grease if needed.
Add the mushrooms: Stir the drained canned mushrooms into the cooked ground beef and heat for 2–3 minutes.
Make the gravy: Prepare the beef gravy according to the instructions on the gravy packet.
Combine: Pour the prepared gravy into the skillet with the ground beef and mushrooms. Stir well to combine and let everything simmer for a few minutes until heated through.
Fill the pita pockets: Carefully open each pita pocket and spoon the beef and gravy mixture inside. Add a generous handful of shredded cheddar cheese.
Toast the pita pockets: Heat a griddle or large skillet over medium heat and lightly butter the surface. Place the filled pita pockets on the pan and cook for a few minutes on each side, gently pressing them down as they cook, until the pita is golden brown and crisp and the cheese is melted.
Serve: Remove from the pan, let cool for a minute or two, and serve warm.