Ok so these are quite impressive looking, but there is quite an amount of skill involved and hand colouring going on so get some disposable gloves or use a stand mixer if you can / electric whisk with dough hook attachments.
First up in a bowl add the flour. Put the yeast and sugar to one side of it and the salt to the other so it does not mix immediately or it can kill the yeast. Add the warm water and mix with a spoon / your fingers, then get really mixing using your hands or a stand mixer to form a dough. If the dough is still a little wet, add more flour and knead through until tacky, but not wet. Place onto a floured surface and knead for 5 minutes until smooth.
Weigh the dough and divide into 5 equal portions. Cover them with a damp tea towel and use 5 separate bowls as you dye each ball the separate colours. A stand mixer or electric whisk would help massively but wear disposable gloves or just get ‘smurf hands’ like I did! You really have to work the colour in, so do it in small batches, then stretch it and turn it to expose any white areas and add more colour in small steps. Each dough colour should take about 5 minutes for a good thorough job! So repeat this in 5 separate bowls, for the 5 separate colours respectively. Washing your hands in between so they do not dye into the next one. Cover with clingfilm each dyed piece of dough in a lightly greased bowl and leave to prove for an hour or until doubled in size.
Turn out the red dough onto a lightly floured work surface and, using a rolling pin, roll out to a 20 x 12cm rectangle. Do not roll it out thin then trim it, use the whole ball of dough to get that 20 x 12 cm shape or as close to it. Repeat with the orange dough, then stack it on top of the red, then carry on with the yellow, green and blue dough in that order to create the rainbow stack of 20 x 12cm.
Slice lengthways into 5 strips, the instructions I had said said 6 strips (20 x 2 cm strips)… make them a little wider for bigger bagels. Slice through all the way so you have long rainbow strips.
To shape the bagels, lay one of the stacked dough strips on your work surface and place the palm of your hands at each end. Simultaneously, gently move your right hand forwards and your left hand backwards to twist the dough into a rope about 26cm long. Pinch the ends together to form a circle and gently roll the join backwards and forwards to seal (bayayayaaa). Repeat with the remaining 4 strips. Or (hint, for perfectionists) wait until you’ve puffed the first one up on bicarb step to determine what size you want to do the rest of them.
Place the bagel(s) on a lined baking sheets, cover with a tea towel and leave to prove for 30 minutes until risen and puffed up.
Heat the oven to 200°C/180°C fan/Gas 6. Meanwhile bring a large saucepan of water to the boil and add the bicarbonate of soda keeping it on a steady simmer. This is what really determines the final size of the bagels. Drop one or two bagels in at a time and cook for about 90 seconds, turning once as you go. They will puff up and increase in size. Put back on the baking sheet and repeat with the others.
Bake the bagels for 25–30 minutes, until cooked through. Remove from the oven and transfer to a wire rack to cool – stonking!