Preheat the oven to 375 degrees F. Combine the heavy cream, thyme, bay leaves, garlic and nutmeg in a medium saucepan. Bring to a gentle simmer over medium heat. Add the spring onion whites and simmer until just starting to soften, about 5 minutes. Season with 1 1/2 teaspoons salt and a few grinds of pepper. Remove the thyme sprigs and bay leaves. Stir in about half of the spring onion greens.
Spread the potatoes in a 9-by-13-inch baking dish. Pour the cream mixture over the top and gently stir, pressing and submerging the potatoes to make an even layer. Cover with foil and bake until the potatoes are tender and the cream is bubbling, 45 to 55 minutes.
Uncover the potatoes and sprinkle with the cheese. Bake until the cheese is golden, 10 to 15 minutes. Let cool 15 minutes. Sprinkle with the remaining spring onion greens just before serving.