Preheat the oven to 400 degrees F. Butter a lasagna pan or other 4-quart baking dish. In a medium saucepan, melt the butter over medium heat. Add the garlic and cook until sizzling, about 1 minute, then pour in the cream and add the bay leaves. Bring to a simmer and remove from the heat.
Toss all of the root vegetables with the sage and thyme in a large bowl and season well with salt and pepper. Layer half of the vegetables in the prepared dish. Sprinkle with half of both cheeses. Layer the remaining vegetables on top. Remove the bay leaves from the hot cream and pour the cream over the vegetables. Sprinkle with the remaining Cheddar and Parmesan. Place the dish on a baking sheet and cover with foil (tenting it, so it doesn't touch the cheese). Bake until the vegetables are just tender and the cream is bubbly, 1 to 1 1/4 hours. Remove the foil and continue to bake until golden on top, about 45 minutes more. Let rest 20 minutes before serving.