Whisk the coconut sauce ingredients together, set aside.
Slice the chicken breasts in the half through the equator to create 4 fillets. Cover with plastic wrap and pound to an even thickness. Pat dry.
Whisk the flour and all chicken seasoning together in a shallow dish. Dredge each breast in the mixture, shake off any excess, then transfer to a dry surface.
Melt the 2 tablespoons butter in 2 tablespoons olive oil in a large skillet over medium-high heat. Once hot, add chicken and cook for 4-5 (depending on thickness) until golden and cooked through. Transfer chicken to a plate, don't wipe out skillet.
Reduce heat to medium and add a drizzle of olive oil if needed. Add white parts of green onions and cook one minute. Add garlic and ginger and cook 30 seconds.
Reduce heat to low and stir in the sauce, scraping up any brown bits on the bottom of the pan. Bring to a simmer until sauce is thickened, 1-2 minutes. Carefully taste (don't burn your tongue!) and adjust to taste, adding additional honey for sweeter or lime juice for tangier.
Add chicken and warm through. Garnish with cilantro and/or basil and green onions. Serve over rice.