Combine the dipping sauce ingredients in a small bowl; set aside.
Combine filling ingredients in a medium bowl; mix well. To shape each potsticker, place 1 teaspoon of filling in center of a potsticker wrapper. Brush edges of wrapper with water; fold wrapper in half, crimping 1 side, to form a semicircle. Pinch edges together to seal. Cover potstickers with a dry towel to prevent drying.
Place a wide frying pan over medium heat until hot. Add 1 to 1/2 tablespoons cooking oil, swirling to coat sides. Add potstickers, half at a time, seam side up. Cook until bottoms are golden brown, 3 to 4 minutes. Add 1/3 cup water; reduce heat to low, cover, and cook until liquid is absorbed, 4 to 5 minutes. Place potstickers, browned side up, on a serving plate; keep warm. Cook remaining potstickers with remaining oil and water.
Garnish potstickers with basil. Serve with dipping sauce.