Melt 4 tablespoons of butter in a pan over medium heat.
Sprinkle with the flour and fry for 3 minutes.
Pour in the milk, little by little, stirring, until it thickens.
Remove from heat, mix the cream and season with salt, pepper and nutmeg. Set aside.
In medium heat, melt the remaining butter in a frying pan, add the broccoli, the carrot and sauté for 3 minutes.
Add the hearts of palm, the spinach and saute for another 2 minutes.
Season with salt and pepper. In a large baking dish, alternate layers of sauce, pasta, sauce again, sauteed and mozzarella cheese, ending with pasta and sauce.
Sprinkle the Parmesan cheese and bake in a preheated medium oven for 40 minutes.
Remove from oven, let it rest for 10 minutes and serve.