Preheat your oven to 375°F (190°C) and lightly brush a 2-quart baking dish with 1 tablespoon of the melted butter.
In a large bowl, combine the sliced potatoes and onions. Drizzle with the olive oil and the remaining 2 tablespoons of melted butter, then sprinkle with the salt and pepper. Toss everything together until the slices are evenly coated.
Arrange half of the potato and onion mixture in an even layer in the prepared baking dish. Pour 1 cup of the warmed broth evenly over the layer.
Arrange the remaining potato and onion mixture over the first layer and pour the remaining 1 cup of broth over the top. The broth should come about halfway up the sides of the potatoes. Place the thyme sprigs on top.
Cover the dish tightly with aluminum foil and bake for 45 minutes. The potatoes should be tender when pierced with a knife.
Remove the foil and continue baking for another 25-30 minutes, or until the top is golden brown and the edges are crispy.