1.In a medium bowl, stir together flour, salt, and yeast; add carrot juice. Using a wooden spoon or your hands, mix until a wet, sticky dough is formed, about 30 seconds. If it's not really sticky to the touch, add another tablespoon or two of water. Add currants and walnuts and mix until incorporated. Cover bowl and let stand until surface is dotted with bubbles and dough is more than doubled in size, 12 to 18 hours.
2.Generously dust work surface with flour. Using a bowl scraper or rubber spatula, scrape dough out of bowl in one piece. Using floured hands or a bowl scraper, lift edges of dough in toward center. Tuck in edges of dough to make a round.
3.Place a clean kitchen towel on work surface. Generously dust towel with flour and sprinkle with cumin seeds. Gently place dough on towel, seam side-down. If dough is tacky, dust top lightly with flour. Fold the ends of the towel loosely over dough to cover and place in a warm, draft-free spot to rise for 1 to 2 hours. Dough is ready when it is almost doubled in size and holds an impression when gently poked with a finger. If it springs back, let rise 15 minutes more.
4.Meanwhile, one half hour before the end of the second rise, preheat oven to 450 degrees with a rack set in bottom third of oven. Place a covered 4 1/2-to-5 1/2-quart cast-iron, high-quality all-ceramic, or enameled cast-iron (with plastic handle removed and screw hole plugged with aluminum foil) in the center of rack.
5.Using pot holders, very carefully remove preheated pot from oven and uncover. Unfold towel and quickly but gently invert dough into pot, seam side-up. Cover pot, return to oven, and bake for 25 minutes.
6.Uncover and continue baking until bread is a deep chestnut color, 15 to 20 minutes more. Using a heatproof spatula or pot holders, carefully lift bread out of pot and place it on a rack; let cool completely.