Preheat the oven to 350° F.
In a large skillet over medium-high heat, melt the butter with the sliced onions. Cook, stirring occasionally, until the onions are softened, about 10 minutes. Then add the vegetable broth and continue cooking for another 5 minutes until the onions are deeply caramelized.
Stir in the garlic and thyme, seasoning with salt and pepper. Cook for an additional 2 minutes, then remove from the heat.
Butter a 9×13-inch casserole dish. In a large glass measuring cup, mix together the cream, milk, cayenne, salt, and pepper. Add the Gruyere cheese into the mixture. Pour one-third of the milk mixture into the bottom of the baking dish. Layer one-third of the potatoes over the milk, followed by half of the caramelized onions. Add another one-third of the milk mixture, then one-third of the potatoes, and the remaining onions. Finish with the last third of the potatoes and pour the remaining milk mixture evenly over the top to cover.
Cover the dish and bake for 1 hour 45 minutes to 2 hours. Remove the foil, sprinkle the cheddar cheese on top, and bake for an additional 20 minutes, or until the cheese is golden and melted. Serve warm, garnished with fresh thyme.