If using yeast: Dissolve the honey or sugar in warm water and sprinkle the yeast over the top. Let it sit for about 5 minutes, or until it becomes frothy.
If using sourdough starter: Mix the starter directly into the warm water.
In a large bowl, combine the rye flour, all-purpose flour, and salt. Add the yeast mixture or sourdough starter mixture.
Stir until a dough forms. The dough will be sticky and dense.
Transfer the dough to a floured surface and knead for about 5-7 minutes, until smooth and elastic. You may need to add a little more flour if the dough is too sticky.
Place the dough in a lightly oiled bowl, cover with a damp cloth or plastic wrap, and let it rise in a warm place for 1-2 hours, or until doubled in size.
Punch down the risen dough and transfer it to a lightly floured surface. Shape it into a round or oval loaf.
Place the shaped loaf on a parchment-lined baking sheet or in a greased loaf pan.
If desired, brush the top with a little vegetable oil and sprinkle with caraway seeds.
Cover the loaf with a cloth and let it rise for about 30-45 minutes, or until it has puffed up.
Preheat your oven to 400째F (200째C).
Bake the loaf for 30-35 minutes, or until the bread sounds hollow when tapped on the bottom and has a deep brown crust.
Allow the bread to cool on a wire rack before slicing.
Enjoy your meal!