Slice zucchini about a 1/4 inch thick length wise or on the diagonal. Grill zucchini until they are well scored on each size (you need to cook out most of the water so that you do not have a watery casserole). Set aside or do a day ahead and refrigerate. You'll need enough zucchini to make two layers (faux noodles) in your dish.
Boil chicken breast in salted water until done. You can reserved the broth from the chicken breast to use in other recipes, and it freezes well. Shred chicken and set aside.
Make the white sauce (The "Low Carb White Sauce" was adapted from the "Step Away From the Carbs" website.). In a large saucepan cook onion in 1 tablespoon of the oil until translucent. Add garlic and cook another minute or two. Add cream cheese, heavy cream and water (or use some of the chicken broth) to the saucepan. Heat over a low heat until the cream cheese has melted. Place an egg yolk into a small bowl and temper it by adding a small spoonful of the cream mixture into the bowl and mixing well. Then add the egg yolk mixture into the saucepan. Keep cooking for a few minutes until the sauce has thickened, stirring constantly. Add salt, pepper, oregano and shredded chicken and cook on low for about 2 minutes. Set aside.
In a food processor combine room temperature cream cheese, cottage cheese, egg and parmesan and blend until well combined. Set aside.
Coat a 9" by 13" pan with olive oil. Cover the bottom of the pan with one layer of zucchini. Add a layer of the cream and chicken mixture. Top with half of the cottage cheese mixture and half of the mozzarella. Repeat the zucchini chicken cheese layers with the remaining ingredients. Back at 350 for 30-35 minutes. Let cook for about 10 minutes before slicing and serving.