Whisk together coconut milk, cornstarch, Asian sweet chili sauce, 3 tablespoons honey (add more later if desired), lime juice, soy sauce, Asian chili sauce, and dried basil in a bowl until smooth; set aside.
Slice each chicken breast in half horizontally to make 4 cutlets, cover with plastic wrap and pound to an even thickness; pat dry with paper towels.
In a shallow dish, whisk together flour, salt, 1/2 tsp ground ginger, 1/2 tsp garlic powder, 1/2 tsp ground coriander, 1/2 tsp turmeric, and 1/2 tsp black pepper. Dredge each chicken cutlet in the flour mixture and shake off excess.
Heat a large skillet over medium-high heat and melt 2 tablespoons butter with 2 tablespoons olive oil. When the pan is hot, add the chicken and cook 4–5 minutes per side (depending on thickness) until golden and cooked through; transfer to a plate and keep the pan drippings.
Reduce heat to medium, add a drizzle of oil if needed, and sauté the white parts of the chopped green onions for about 1 minute. Add minced garlic and grated fresh ginger and cook 30 seconds until fragrant.
Reduce heat to low and pour in the prepared coconut sauce, scraping up any browned bits from the pan. Simmer 1–2 minutes until the sauce thickens. Taste and adjust with additional honey for sweetness or lime juice for tang.
Return the chicken to the skillet and warm through in the sauce for 1–2 minutes. Garnish with sliced fresno or jalapeño peppers, chopped cilantro, and sliced green onion greens; serve over rice.