1. In a large bowl combine buttermilk, the water, yeast, and honey. Stir until yeast dissolves and let stand for 5 minutes.

2. In a small bowl beat eggs, then add to yeast mixture. Stir in 5 to 6 cups of flour, or enough to form a thick batter. Stir well and let stand 20 minutes.

3. Stir batter vigorously for 1 minute, then add 2 tablespoons of the oil and enough flour to form a thick dough. Lightly flour a counter or breadboard and turn dough onto board. Knead until smooth and elastic (5 to 10 minutes). Lightly oil a mixing bowl and put kneaded dough into it. Cover bowl with a dish towel and let rise for 40 minutes.

4. Punch dough down, then cover again and let rise an additional 30 minutes.

5. While dough is rising the second time, combine remaining oil, sauerkraut, carrots, pepper, and salt substitute in a small saucepan. Cook this mixture uncovered, over medium-high heat, for 10 minutes, stirring frequently. Remove from heat and pour into a colander set over the sink. Let sauerkraut drain for 10 minutes.

6. Lightly oil a 9- by 12-inch baking pan and preheat oven to 350 degrees F. Separate dough into 2 balls and roll each into a 9- by 12-inch rectangle. Place one rectangle into the baking pan. Spoon sauerkraut mixture on top of it. Place second rectangle of dough on top of sauerkraut. Reach into pan and pinch edges of bottom and top layers of dough together, sealing tightly. Let it rise for 10 minutes.

7. Bake sauerkraut bread until browned (about 45 minutes). It should lift easily out of the pan. Let cool on a rack, and then slice into thick wedges.