In stand mixer bowl, add 1 3/4 cups bread flour, yeast, sugar, salt, caraway and dill seed; mix well. In saucepan or microwave-safe dish, heat milk, water and shortening until warm (120°-130°F; shortening does not need to melt). Add to flour mixture. Using a paddle attachment, blend on low speed for 30 seconds. Beat on medium speed for 3 minutes.
Switch to dough hook attachment. Gradually stir in rye flour and enough remaining bread flour to make a firm dough. Knead until smooth and elastic, about 5 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.)
Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
Punch down dough. Divide into 2 parts. On lightly floured surface, roll or pat each half to a 14x7-inch rectangle. Starting with shorter side, roll up tightly, pressing dough into roll with each turn. Pinch edges and ends to seal. Place in greased 8½x4½-inch bread pans. Cover; let rise in warm place until indentation remains after lightly touching, about 30 minutes.
Preheat oven to 375°F.
Bake for 30 to 40 minutes or until golden brown. Cool in pans for 10 minutes. Remove breads from pans and finish cooling on wire rack.