In a large skillet over medium heat, cook the chicken breast until browned and cooked through, turning once. The internal temperature should reach 165°F. Remove the chicken from the skillet and let cool until you’re able to shred it.
Return the shredded chicken to the skillet. Add the soy sauce, sesame oil, garlic, ginger, green onions, cabbage, and carrots. Stir and cook for 1 minute.
Add the hoisin sauce to the skillet and stir to coat the chicken and vegetable mixture evenly. Remove from heat.
Fill the center of each wonton wrapper with the chicken mixture.
Fold the wrapper in half diagonally to form a taco. There’s no need to press the edges together or seal.
Add about 3 tablespoons of oil in a separate pan over medium-high heat. When the oil starts to shimmer, it’s ready.
Carefully place the filled wontons in the hot oil and fry for 1-2 minutes on each side and the fold, until golden brown and crispy. Use a slotted spoon to transfer the fried wonton tacos to a paper towel-lined plate to drain any excess oil.
Serve immediately with optional toppings.