In a medium saucepan, combine buttermilk, the 1/2 cup water, the brown sugar, molasses, orange peel, caraway seed, anise seed, and salt. Heat, stirring occasionally, until brown sugar dissolves and the mixture is just warm (120 degree F to 130 degree F).
In a large bowl, combine yeast and the 1/4 cup warm water, stirring to dissolve the yeast. Let stand until mixture is bubbly.
Stir in the egg and 1-1/2 cups of the unbleached flour. Add half of the buttermilk mixture; stir until combined. Stir in rye flour. Add remaining buttermilk mixture and stir well. Stir in as much remaining unbleached flour as you can.
Turn dough out onto a lightly floured surface. Knead in enough remaining unbleached flour to make a dough that's smooth and elastic (about 6 to 8 minutes total).
Place the dough in a greased bowl, turning once to grease surface of dough. Cover and let the dough rise in a warm place until doubled in size (about 1-1/4 to 1-1/2 hours).
Lightly coat a large baking sheet with nonstick cooking spray and set aside. Punch dough down. Let rest for 10 minutes. Shape into fifteen 2-inch balls (a little larger than golf balls). Place the balls of dough on a prepared baking sheet about 2 inches apart.
Cover and let rise in a warm place until nearly doubled in size (about 30 to 45 minutes). If you like, in a small bowl, combine egg white and the 1 tablespoon water. Brush egg white mixture over the rolls. Sprinkle with additional caraway seed, if you like.
Bake rolls in a 375 degree F oven for 12 to 15 minutes or until golden brown. Remove rolls from the baking sheet. Cool on wire racks. Serve rolls warm or cooled. Makes 15 rolls.