Kurnik: Russian Chicken Pie

Name: Kurnik: Russian Chicken Pie
Cuisine: European, Eastern European
Ingredients: 4 ounces butter (cold, cut into chunks); 4 ounces cream cheese (cold, cut into chunks); 1 cup all-purpose flour; 2 cups water (or chicken broth); 1 cup rice (rinsed); 2 large onions (thinly sliced); 8 ounces mushrooms (sliced); 2 tablespoons butter; 1 cup half-and-half; 1 tablespoon cornstarch; 1 cup chicken broth; 3 cups cooked chicken meat (diced); 2 tablespoons parsley (chopped); 1 teaspoon salt; Black pepper (to taste); 4 hard-cooked eggs (finely chopped); 1 tablespoon dill (chopped); 1 egg yolk; 1 tablespoon water (beaten)