Place the silken tofu in a food processor and blend until completely smooth and creamy.
Transfer the puréed tofu to a medium bowl.
Add the chopped chives, minced ginger, and sesame oil to the bowl with the tofu.
Season generously with salt and pepper, and stir until everything is well combined.
To assemble, place a wonton wrapper on a clean surface. Spoon about 1 scant tablespoon of the tofu filling into the center. Moisten the edges of the wrapper with a little water using your finger or a pastry brush.
Fold the wrapper into a triangle, pressing the edges together firmly to seal.
Make sure to press out any trapped air pockets.
Set the finished wonton on a lightly floured plate or a sheet of wax paper and repeat with the remaining wrappers and filling.
Pour at least 2 inches / 5 cm of neutral oil into a deep pan or deep-fryer and heat over medium-high heat to 350°F / 175°C.
Working in small batches to avoid crowding the pan, gently lower the wontons into the hot oil.
Fry for 3-5 minutes, turning once, until they are golden brown and crisp.
Use a slotted spoon to remove the wontons from the oil and let them drain on a wire rack or a plate lined with paper towels.
Serve immediately with your favorite dipping sauce.
Don't overfill the wrappers! A scant tablespoon is all you need to prevent them from bursting while frying.