Heat the oven to 400°F and grease a 9 x 13-inch baking pan with 2 tablespoons of the butter. Bring a stockpot of water to a boil and salt it.
Put the milk and the bay leaves in a small saucepan over medium-low heat. When small bubbles appear along the sides of the pan, after about 5 minutes, turn off the heat and let the milk sit. When the water boils, cook the pasta to the point where it is just becoming tender but is still quite underdone and firm in the center. Start tasting after 3 minutes. Drain the pasta and rinse it quickly in cold water to stop the cooking.
Fish the bay leaves out of the milk. Spread a third of the pasta evenly in the prepared baking dish. Sprinkle it with half of the fl our (using your hands is easiest), dot with half of the remaining butter, cover with 1/2 cup of the cheddar, and sprinkle with salt and pepper.
Repeat this process once more. Finally, spread out the last of the pasta and top with the remaining cheddar and the Parmesan; sprinkle with the bread crumbs. Pour the heated milk over all. Bake until bubbling and browned on top, 30 to 40 minutes. Serve immediately.