Begin the rye sour starter: In a large bowl combine the rye flour, active dry yeast, warm water (110 degrees F), crushed caraway seeds and minced onion; stir with a wooden spoon until smooth. The mixture should be thin and soupy. Cover with plastic wrap and allow to stand in a warm spot until bubbly and fermented, up to 24 hours.
Prepare Stage One: In a large bowl combine the water, 1¼ cups of the flour, and the starter; stir with a wooden spoon until smooth. The mixture should pull slightly and may start to come away from the sides of the bowl. Wipe down the sides of the bowl and sprinkle the remaining ¼ cup flour over the entire surface of the sour. Cover with plastic wrap and let stand in a warm place until doubled in size and the floured top appears cracked with wide openings, about 4 to 8 hours. Avoid letting the mixture collapse.
Prepare Stage Two: To the Stage One sour add the water and ¾ cup of the flour; mix until smooth. Wipe down the sides of the bowl and sprinkle the remaining ¼ cup flour over the entire surface of the sour. Allow to rise in a warm area until doubled in size, about 4 to 8 hours.
Prepare Stage Three: To the Stage Two sour add the water and the 1 cup flour; mix until smooth. Add more flour, ¼ cup at a time, until a dough-like consistency is reached. Cover with plastic wrap and leave in a warm spot until doubled in size, about 4 to 8 hours. At this point the starter is ready to be used in the bread.
The caraway seeds can be ground in a coffee or spice grinder or with a mortar and pestle before adding to the starter.
When preparing Stages One and Two aim for a thick consistency as close as possible to that of a soft dough; if the mixture is too soupy, add more flour ¼ cup at a time and mix until smooth.
Timing recommendation: prepare Stages One and Two on the same day, refrigerate the second stage overnight if desired, and prepare Stage Three the morning of baking. If you plan to bake first thing in the morning, prepare Stage Three the evening before so it can rise slowly overnight.