Combine chicken breast, water, and chicken bouillon in a large pot; bring to a boil and cook until chicken is no longer pink, 20 to 30 minutes.
Remove chicken to a cutting board, reserving broth. Shred chicken using 2 forks.
Preheat oven to 400 degrees F (200 degrees C).
Whisk 2 cups plus 1 1/2 tablespoon milk, egg yolks, and all-purpose flour into the reserved broth. Bring to a boil; cook, stirring constantly, until thickened, about 5 minutes. Stir in shredded chicken and corn. Remove from heat and whisk in cream.
Pour chicken mixture into a baking dish. Spread cottage cheese on top and cover with sliced mozzarella cheese.
Bake in the preheated oven until mozzarella cheese is melted, 10 to 15 minutes.