Easy Lithuanian Dark Rye Bread (Rugine Duona)

Name: Easy Lithuanian Dark Rye Bread (Rugine Duona)
Prep time: 20 min
Cook time: 1 h
Total time: 1 h 20 min
Cuisine: Eastern European
Ingredients: 2 cups milk; 2 tablespoons butter; 2 tablespoons sugar; 1 teaspoon kosher salt; 1 package active dry yeast; 1/2 cup lukewarm water; 4 cups dark rye flour , divided; 2 1/2 cups whole-wheat flour; 2 tablespoons caraway seeds, optional; 1 large egg white, beaten