Grease a 9 by 13-inch baking dish with a tablespoon of softened butter. Set aside. For the Custard: In a large mixing bowl, whisk together all the ingredients except the half-half. Add the half-half last and mix until well blended. Set aside. For the Sautéed Onions and Garlic: In a sauté pan over medium heat, melt the butter. Add the onions and cook for 5 minutes or until soft. Add the garlic and sauté until fragrant. Season with salt. Set aside. To assemble: Lay half the amount of bread cubes at the bottom of the buttered baking dish. Then, half the amount of Canadian bacon, Gruyere cheese, Swiss cheese, sautéed onions and garlic mixture. Pour half the amount of the custard mixture. Repeat with the remaining half of the ingredients. Press lightly to ensure that the bread is thoroughly submerged in the custard. Sprinkle fresh thyme leaves on top. Let it soak in the refrigerator for at least 2 hours or overnight. Next day, bake at a preheated 375 degree Fahrenheit oven for 45 minutes to 1 hour or until puffy and golden brown on top. Before serving, cook a fried egg and place it on top. Enjoy!