Set yeast according to package directions. Heat milk and butter just until warm. In a bowl mix sugar and salt, 1 whole egg and 1 egg yolk (save egg white), beat eggs and sugar and salt; add milk and butter, slowly add enough flour to make a soft dough, add yeast and bananas. Add more flour until the dough is too stiff to stir easily. Turn onto floured surface and knead until the dough is moderately stiff. Shape into a ball and place in a greased bowl and let rise until about double in size. Divide dough in half and shape into loaf and place each in a greased loaf pan and let rise until doubled in size. Brush top with egg white and the 1 teaspoon water, mixed. Bake at 350 degrees for 35-40 minutes.