Preheat the Oven: Begin by preheating your oven to 350°F (175°C). This ensures the oven reaches the proper temperature by the time the casserole is assembled and ready to bake.

Caramelize the Onions: In a large skillet over medium-low heat, melt 2 tablespoons of butter along with the olive oil. Add the thinly sliced onions and dried thyme. Cook the onions slowly, stirring occasionally, for approximately 30 minutes, or until they are deeply golden brown and caramelized. Once done, remove the onions from the skillet and set them aside.

Prepare the Roux: Increase the heat to medium and add the remaining 4 tablespoons of butter to the skillet. Once melted, add the minced garlic and cook for 1 minute, stirring frequently. Use a silicone spatula to scrape the bottom and sides of the skillet to incorporate any flavorful bits. Add the flour and whisk continuously for about 1 minute, or until the raw flour aroma dissipates.

Create the Cheese Sauce Base: Gradually add the milk to the skillet, pouring it in small splashes while whisking constantly to ensure a smooth mixture. Adding the milk too quickly may cause the roux to thin out unevenly. Once all the milk is incorporated, bring the mixture to a gentle boil, then remove it from the heat.

Season the Sauce: Stir in the mustard powder, salt, black pepper, and cayenne pepper until fully combined. Allow the sauce to cool slightly before proceeding to the next step.

Incorporate the Cheese: Reserve 1 heaping cup of shredded cheddar cheese for topping the casserole later. Gradually sprinkle the remaining shredded cheddar into the sauce, stirring until melted and smooth. Avoid adding the cheese to an overly hot base, as this may cause the dairy to separate and result in a grainy texture. Once the cheddar is fully incorporated, stir in the softened cream cheese until the sauce is velvety and uniform. Finally, fold in the caramelized onions.

Prepare the Potatoes: Peel the Yukon Gold potatoes and rinse them thoroughly. Pat them dry with a clean kitchen towel. Using a sharp knife or mandoline slicer, cut the potatoes into thin, even slices approximately 1/8-inch thick.

Assemble the Casserole: Lightly grease a 9 x 13-inch baking dish. Arrange half of the potato slices in an even layer on the bottom of the dish. Pour half of the cheese sauce over the potatoes, spreading it evenly. Repeat with the remaining potatoes and cheese sauce. Finally, sprinkle the reserved 1 cup of shredded cheddar cheese over the top.

Bake the Casserole: Cover the baking dish with aluminum foil and bake in the preheated oven for 45 minutes. After 45 minutes, remove the foil and continue baking for an additional 40 minutes, or until the potatoes are tender and the top is golden brown.

Optional Broiling Step: For a more deeply browned and crispy top, switch the oven to broil at 400°F (200°C) and broil the casserole for 2-3 minutes. Monitor closely to prevent burning.

Rest and Serve: Remove the casserole from the oven and allow it to rest for 5-10 minutes before serving. This resting period helps the sauce set slightly, making it easier to slice and serve. Garnish with fresh parsley, if desired, and enjoy.