Mix the flour, salt and yeast in a bowl. Combine the carrot juice with all the other ingredients up to and including the butter, knead to form a soft, smooth dough. Cover and leave to rise at room temperature for approx. 1½ hrs. until doubled in size.
Place the dough on a lightly floured surface, do not knead any more, shape into a roll. Divide the dough into 20 portions and shape them into balls. Make a hole in the middle of each with a lightly floured wooden spoon handle. Allow the dough rings to form around the handle until an opening approx. 4 cm in diameter is created. Place the bagels on a baking tray lined with baking paper, cover and leave to rise for approx. 15 mins. Cook approx. 3 bagels at a time in just-boiling salted water for approx. 12 seconds. Remove with a slotted spoon, drain thoroughly and return to the baking paper. Coat bagels with a little egg yolk, poppy seeds, sesame or sunflower seeds.
Approx. 15 mins. in the centre of an oven preheated to 220°C. Remove from the oven, leave to cool on a cooling rack.
Cut the bagels in half crosswise, spread with cream cheese or peanut butter. Top bagels with the remaining ingredients as desired.