Step 1: Preparation is Key

1. Preheat and Prep: Adjust your oven rack to the middle position and preheat to 400°F (200°C). Generously butter your 9×13 inch baking dish. This not only prevents sticking but also adds a little extra flavor and helps the bottom brown nicely.
2. Vegetable Prep: Wash, peel, and slice your potatoes to a uniform 1/8-inch thickness. A mandoline slicer is your best friend here for consistency, which ensures even cooking. If you don’t have one, use a sharp knife and take your time. Place the sliced potatoes in a large bowl of cold water to prevent them from browning while you prepare the other components.
3. Chop Remaining Veggies: Prepare your carrot, broccoli, bell pepper, onion, and garlic as described in the ingredients list. Having everything chopped and ready (a process called “mise en place”) makes the cooking process smooth and stress-free.

Step 2: Crafting the Velvety Cheese Sauce

1. Sauté Aromatics: In a large saucepan or Dutch oven, melt the 4 tablespoons of butter over medium heat. Add the finely chopped yellow onion and cook, stirring occasionally, until it has softened and become translucent, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant. Be careful not to burn the garlic.
2. Make the Roux: Sprinkle the 4 tablespoons of all-purpose flour over the cooked onions and garlic. Stir constantly and cook for about 60-90 seconds. This step is crucial to cook out the raw flour taste and forms the thickening base for our sauce. The mixture will look like a thick, clumpy paste.
3. Build the Sauce: Slowly whisk in the vegetable broth first. This helps to break up the roux smoothly. Then, while continuing to whisk, gradually pour in the whole milk and heavy cream. A slow, steady stream while whisking is the secret to a lump-free sauce.
4. Season and Thicken: Add the dried thyme, paprika, salt, and black pepper. Continue to cook, stirring frequently, until the sauce comes to a gentle simmer and has thickened enough to coat the back of a spoon. This should take about 5-8 minutes.
5. Melt the Cheese: Remove the saucepan from the heat. Add 1 cup of the shredded cheddar and 1/2 cup of the shredded mozzarella to the sauce. Stir until the cheese is completely melted and the sauce is smooth and luxurious. Taste the sauce and adjust seasoning if necessary. It should be well-seasoned, as the potatoes will absorb a lot of the salt.

Step 3: Assembling and Baking Your Masterpiece

1. Combine Components: Drain the potato slices thoroughly and pat them dry. Add the dry potatoes, sliced carrots, broccoli florets, and diced bell pepper to a very large mixing bowl.
2. Coat in Sauce: Pour the prepared cheese sauce over the vegetable and potato mixture. Use a large spatula to gently fold and mix everything together until every slice of potato and every vegetable is evenly coated in the glorious sauce.
3. Layer in Dish: Carefully transfer the mixture into your prepared 9×13 inch baking dish. Spread it out into an even layer.
4. Top with Cheese: Sprinkle the remaining 1 cup of cheddar cheese and 1/2 cup of mozzarella cheese evenly over the top of the casserole.
5. First Bake (Covered): Cover the baking dish tightly with aluminum foil. This traps the steam and is essential for cooking the potatoes and vegetables all the way through until they are tender. Bake in the preheated 400°F (200°C) oven for 45 minutes.
6. Second Bake (Uncovered): After 45 minutes, carefully remove the foil. The bake will look pale and steamy. Return the dish to the oven, uncovered, and bake for an additional 20-30 minutes, or until the top is deeply golden brown, bubbly, and a sharp knife or skewer inserted into the center meets very little resistance.
7. Rest Before Serving: This is a critical step! Let the vegetable potato bake rest on a wire rack for at least 10-15 minutes before serving. This allows the sauce to set up slightly, making it easier to slice and serve. Cutting into it immediately will result in a runny sauce.