In large bowl, combine 2 cups all-purpose flour, sugar, undissolved yeast, caraway seed and salt. Gradually add very warm water and oil to dry ingredients; beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add 1/2 cup all-purpose flour; beat 2 minutes at high speed, scraping bowl occasionally. With spoon, stir in rye flour and enough remaining all-purpose flour to make soft dough. Knead on lightly floured surface until smooth and elastic, about 6 to 8 minutes. Place in greased bowl, turning to grease top. Cover; let rise in warm, draft-free place until doubled in size, about 30 to 45 minutes (With Rapid Rise Yeast, cover kneaded dough and let rest on floured surface 10 minutes. Proceed with recipe). Punch dough down. Remove dough to lightly floured surface; divide dough in half. Form each into 5-inch ball. Place on large greased baking sheet. Cover; let rise in warm, draft-free place until doubled in size, about 30 to 45 minutes. With sharp knife, make 4 slashes (1/4-inch deep) in crisscross fashion on top of each loaf. Brush with egg white mixture. Bake at 400 degrees F for 35 minutes or until done; cover with foil halfway through baking time to prevent excess browning. Remove from sheet; cool on wire rack