Cook egg noodles in a large pot of boiling water, just until al dente, or even 1-2 minutes less. (The noodles will continue to cook later, when baked). Drain, rinse with cold water and set aside.
Preheat oven to 350 degrees F.
Melt butter in an extra large saucepan over medium to medium high heat. Add flour, salt, pepper, garlic powder, dried basil. Cook, stirring, for 1-2 minutes.
Slowly whisk in chicken broth, about a cup at a time, until mixture is thickened, about 5-10 minutes. Remove from heat.
In a large mixing bowl stir together cottage cheese, egg, 1 cup of mozzarella cheese, and ½ cup parmesan cheese.
Add chicken, noodles and cheese mixture to the saucepan and stir to combine. Taste and add additional salt, pepper or dried basil, if needed.
Pour mixture into a 9×13'' baking dish (or you can bake it right in an oven-safe saucepan it is in). Top with remaining mozzarella and parmesan cheese.
Bake, uncovered, for 30-40 minutes or until golden on top and bubbly. Cool for 10-15 minutes before serving.