In a large mixing bowl, combine the ground chicken, green onions, grated carrots, garlic, ginger, soy sauce, sesame oil, and sriracha. Mix well until all ingredients are thoroughly combined.
Place a wonton wrapper on a clean surface. Spoon about 1 teaspoon of the chicken mixture into the center of the wrapper. Dip your finger in the beaten egg and moisten the edges of the wrapper.
Fold the wrapper in half to create a triangle, pressing out any air. Seal the edges tightly.
Repeat the process with the remaining wrappers and filling.
In a large skillet, heat about 1/4 inch of vegetable oil over medium heat. Once the oil is hot, carefully add the wontons in batches, making sure not to overcrowd the pan.
Fry for about 3-4 minutes on each side or until golden brown and crispy.
Remove the wontons from the skillet and place them on a paper towel-lined plate to drain excess oil.
Serve hot with your favorite dipping sauce, such as sweet chili sauce or soy sauce.