Preheat the oven to 350 degrees F (175 degrees C).

Place potatoes and sweet potatoes in a large baking dish. Mix in onion. Add 1 to 1 1/4 cups vegetable both.

Bake in the preheated oven until potatoes start to soften, about 20 minutes. Remove from oven and add Gruyere cheese. Pour in more vegetable broth if casserole looks dry.

Return to the oven and continue baking until potatoes are tender, about 30 minutes. Stir and serve hot.