Dry the surface of the golden tilefish fillets with paper towels, then season them with a dusting of salt and white pepper. Heat the oil in a large sauté pan over high heat. Sear the fillets until golden brown, just about two minutes. Turn the fillets over, lower the temperature to medium-high, add the butter, and cook for another two minutes. Remove the fillets from sauté pan, place on paper towels, and pat completely dry.
To serve, divide the edamame and baby shiitake mushrooms between four dinner bowls. Place the seared golden tilefish on top of the edamame and shiitake mushrooms, then ladle the hot coconut broth around the fish. Garnish with cilantro leaves, add a swirl of mint oil, and serve immediately.