Heat the olive oil in a deep 12-inch skillet over medium-high heat.
Add the ground chicken, diced sweet onion, grated ginger, and grated garlic to the hot skillet.
Break up the chicken with a spatula and cook, stirring occasionally, until no longer pink, about 5–10 minutes.
Stir in the soy sauce, hoisin sauce, and chili garlic sauce until evenly combined.
Add the coleslaw mix and sauté just until the cabbage and carrots are softened but still slightly crisp, about 2–4 minutes.
Remove the skillet from heat and stir in the sliced green onion greens and minced cilantro.
Serve topped with crispy wonton strips if desired.
