Heat milk, water, and honey until steaming but not boiling. Stir in caraway seeds and oil. Let cool to 115°F or until just warm.
Combine bread flour, rye flour, salt, and yeast in a large bowl or stand mixer bowl.
Add warm liquid mixture and stir until a rough dough forms. Place on stand mixer.
Knead for 6 to 7 minutes until smooth and pulling away from the bowl. It will be slightly sticky. If kneading by hand, knead for 6 to 7 minutes, or until smooth and slightly sticky.
Shape into a ball, place in a greased bowl, cover, and let rise for 20 minutes.
Flatten into a rectangle, fold sides in, and roll into a tight log.
Place seam side down in a greased 9 inch loaf pan. Cover and let rise while oven preheats to 375°F.
Brush with egg wash and slash the top 3 times diagonally about ¼ inch deep.
Bake 30 to 35 minutes, until internal temperature reaches 190°F to 200°F.
Cool 5 minutes in pan, then transfer to a rack to cool completely before slicing.