Make the Thai sauce by whisking together sweet chili sauce, rice vinegar, coconut milk, brown sugar, pressed garlic, peanut butter, grated ginger, lime juice, and soy sauce until fairly smooth.
Spoon out 1/4 cup of the sauce and set aside for brushing and tossing; transfer the remaining sauce to a small saucepan, bring to a boil, then simmer 3–4 minutes until slightly thickened; remove from heat and set aside.
In a large bowl, combine the ground turkey, salt, pepper, sliced green onions, 1/4 cup shredded carrots, and 2–3 tablespoons of the reserved 1/4 cup sauce; mix gently until just combined, avoiding overworking the meat.
Form the mixture into 4 even patties, pressing gently to hold their shape (the mixture will be moist).
Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the patties and cook 4–5 minutes until edges brown and they release easily, then flip and cook another 4–5 minutes until cooked through (internal temperature 165°F / 74°C).
While burgers cook, make the slaw by tossing chopped napa cabbage, 3/4 cup shredded carrots, chopped cilantro, and chopped peanuts with 3–4 tablespoons of the reserved sauce; add more sauce if desired.
Toast the whole wheat buns if desired. Place each cooked burger on a bun, top with a heaping spoonful of slaw and additional sauce as desired, then serve.