Position rack in upper third of oven. Preheat oven to 400°F. Combine green onions, ¼ cup cilantro, lime juice, soy sauce, vinegar, and ginger in small bowl. Whisk in 1½ tablespoons oil. Season with salt and pepper. Set aside. Heat remaining 2 tablespoons oil in large, oven safe skillet over high heat until shimmering. Working in batches if needed, add bok choy, cut-side down. Sear until golden brown, 2 to 4 minutes. Turn cut-side up (and return all Bok Choy to skillet cut-side up if working in batches). Remove skillet from heat. Add wine or sake. Season flounder with salt and pepper. Arrange in single layer over bok choy. Roast in oven until flounder is just cooked through, 8 to 10 minutes. Spoon sauce from bottom of skillet into 4 shallow bowls, dividing evenly. Add bok choy to each bowl, dividing evenly. Top each bowl with flounder fillet. Spoon some cilantro-lime sauce over flounder. Garnish with cilantro sprigs. Pass remaining cilantro-lime sauce for drizzling. Serves 4.