Preheat the oven to 300 degrees. In a bowl, combine the garlic, serrano chile, cilantro, and chopped mint. Season generously with salt and pepper. Cut a shallow 3-by-1 1/2-inch pocket in the wide side of each flounder fillet. Spoon 1 teaspoon of the herb mixture into each pocket.

In a small saucepan, heat the olive oil. Add the cream, yogurt, and the remaining herb mixture and simmer over moderate heat until slightly thickened, about 3 minutes. Remove from the heat.

In a large skillet, heat the 1 tablespoon of vegetable oil. Add the ginger in a single layer and cook over moderately high heat until browned and crisp, about 30 seconds. Tilt the skillet and transfer the ginger to a plate using a slotted spoon. Add the mint leaves to the skillet and cook until crisp, about 10 seconds. Add the mint to the ginger.

In the same skillet, heat 1/4 inch of vegetable oil. Season the flounder with salt and pepper. Dredge 2 fillets in flour and shake off the excess. Fry the flounder over moderately high heat until golden brown, 3 minutes per side. Transfer to a large rimmed baking sheet and repeat with the remaining flounder fillets. Transfer the baking sheet to the oven to keep the fish warm.

Reheat the herbed cream sauce and season with salt. Spoon the sauce onto plates and set the flounder fillets on top. Scatter the fried ginger and mint over the fish and serve right away.