Special equipment: a 13 by 9-inch pan
Preheat the oven to 350 degrees F. Lightly butter a 13 by 9-inch pan.
In a large bowl soak noodles in hot tap water until soft and slightly pliable; about 10 to 15 minutes. Drain the water and set them aside.
In a small microwavable bowl, mix together 2 tablespoons butter, 1 teaspoon paprika, and the red pepper flakes. Microwave for 30 seconds to melt the butter. Add the panko, 1/4 cup grated Parmesan and the parsley. Mix well and set aside.
In a large saucepan over medium-high heat, add oil. Gently add the broccoli and cauliflower. Stir in the zucchini and squash, and a pinch of salt and pepper. Add 2 tablespoons butter and the onions and saute until translucent. Whisk in 2 teaspoons of cracked black pepper, 1 teaspoon paprika, the flour and 1 tablespoon of garlic. Add the milk and vegetable stock and season with salt, to taste. Whisk together and allow to simmer for a few minutes, then stir in the remaining 1/4 cup of grated Parmesan.
Ladle some of the sauce into the bottom of the prepared pan, then add a layer of noodles, then some vegetables and some more sauce. Add another layer of noodles, then the cottage cheese, then vegetables, then some mozzarella and sauce again. Repeat and finish with a layer of noodles. Cover with the remaining sauce and top with the panko mixture. Cover with foil and bake for 30 to 35 minutes. The last 10 minutes, remove the foil to get a crunchier crust. Remove from the oven and allow to rest before cutting and serving.