Moisten the edges of the gyoza wrapper with water so the two sides will stick together. Place a couple small pieces of thinly sliced Wagyu beef in the center of the wrapper and top with a sprinkling of black pepper.
To make the crescent shape: Pinch one end shut and begin to create pleats on one side of the wrapper. Use your index finger to keep ingredients inside while you begin to fold. Make the folds as even as possible, handling the wrapper gently until all pleats are made.
Wrap these dumplings tightly. You don't want a single succulent bite to escape. Repeat with remaining wrappers and ingredients.
Place a thin, nonstick pan over medium heat. To form the "blossom," cluster the gyoza tightly in the pan. Sprinkle with oil. Once you add oil to the dumplings, the sound will change.
After the oil, add 2 teaspoons of boiling water. (Never use cold water, unless you want to create a delicate connective crust. To do this add cold water with 1/2 teaspoon of kyorikiko flour stirred in.) Cover the pan and let the gyoza steam, shaking the pan lightly so they cook evenly.
To finish, remove the lid and add a drizzle of oil once again. Once they're cooked, transfer the gyoza to a warm plate and keep them uncovered so they don't get soggy. Serve as soon as possible with fresh rosemary sprigs and desired barbecue sauce.