Soften Wrappers: Remove dumpling wraps from the refrigerator. Let stand at room temperature (in the package) to soften for 40-60 minutes.
Make Filling: Stir together raw beef, ginger, sesame oil, and salt in a large mixing bowl until combined into a smooth and sticky mixture. Stir in scallions.
Wrap Dumplings: Set aside a small dish of water. Scoop about 1 tablespoon of beef filling onto a single wrapper. Dip finger into water and run it along round edges of wrapper to moisten. Fold the top two sides together and pinch. Fold up the bottom half of the dumpling and pinch again to form a triangle shape. Use more water if needed. Repeat until beef filling is used up. Drape a damp paper towel over the assembled dumplings to avoid drying out.
Pan Fry: Heat oil in a nonstick pan over medium heat for a few minutes until hot. Add dumplings to pan in a single layer and cook until browned on bottom, about 5 minutes. Pour about 2 tablespoons of water over dumplings and immediately cover with a lid until cooked through, about 5 minutes. Work in batches if the pan cannot fit all simultaneously.
Combine the dipping sauce ingredients in a bowl.
Serve: Uncover and transfer cooked dumplings to serving plates. I recommend to drizzle a little bit of sauce over the dumplings and reserve the rest with the remaining dipping sauce.