In a medium pot, bring salted water to a boil over medium heat. Add the plantain chunks and boil for 10-12 minutes. Drain the plantains when cooked.
Allow the plantains to cool slightly, then peel off the skins.
Using a potato masher or fork, roughly mash the plantains into a chunky consistency. Season with salt and black pepper, then set aside.
In a frying pan over medium heat, melt the butter along with the minced garlic. Stir in the flour, ensuring the butter and flour combine smoothly.
Gradually add the milk while stirring continuously. Season with salt, black pepper, nutmeg, and add the thyme sprigs. Let the sauce thicken for 5-7 minutes, stirring constantly.
The sauce is ready when it coats a cooking spoon, and running your finger along the back of the spoon leaves a clear line.
Preheat your oven to 350°F (175°C). Grease a 9×9 inch baking dish and set aside.
Layer half of the mashed plantain in the prepared baking dish. Pour half of the béchamel sauce over the plantain, then sprinkle with half of the cheddar cheese. Repeat the layers with the remaining plantain, sauce, and cheese.
Bake for 20-30 minutes, then let the dish cool for 10 minutes before serving.