Preheat the oven to 400 degrees F. Bring a large pot of water to a boil and salt it.
Cook the milk with the bay leaves in a small saucepan over medium-low heat. When small bubbles appear along the sides, about 5 minutes later, turn off the heat and let stand.
In the salted water, cook the pasta al dente. Drain it, rinse it quickly to stop the cooking, and put it in a large bowl.
Trim the stems from the kale. Bring a large pot of water to boil and add kale. Boil kale for one minute, remove, and set aside to cool. Squeeze excess water from kale and chop into edible pieces.
In a small saucepan over medium-low heat, melt 3 tablespoons of the butter; when it is foamy, add the flour and cook, stirring, until the mixture browns, about 5 minutes. Remove the bay leaves from the milk and add about 1/4 cup of the milk to the hot flour mixture, stirring with a wire whisk all the while. As soon as the mixture becomes smooth, add a little more milk and continue to do so until all the milk is used up and the mixture is thick and smooth. Add the cheddar and stir.
Pour the sauce over the noodles, toss in the Parmesan and kale, mix in the white beans, and sprinkle with salt and pepper.
Use the remaining 1 tablespoon butter to grease a 9 x 13-inch or similar-size baking pan and turn the pasta mixture into it. Top liberally with bread crumbs and bake until bubbling and the crumbs turn brown, about 15 minutes. Serve piping hot.