Mix dry ingredients. Add yeast and water, and mix until the dough starts to come together and then knead for about 10-15 minutes. I do 10 minutes in the machine.
Shape into eight balls and poke a hole in the middle to make shape. Refrigerate overnight.
In the morning, take balls out of fridge and let warm up. They are ready for boiling when they float in a bowl of room temp water. This takes a minimum of 20 minutes, sometimes as long as 90.
Heat oven to 450 °F. Place bagels in pot of boiling water for 30-60 seconds until they "puff" a tad.
Remove from water, and put on a baking sheet that is lined with parchment paper. Bake for about 10-15 minutes.
High gluten flour contains 14% or more protein which is even higher in protein than bread flour (11-13%). If you cannot get high gluten flour, you can adjust the protein content of all-purpose or bread flour (which also is usually bromated and has other additives such as malted barley and ascorbic acid as yeast enhancers) with vital wheat gluten to obtain the desired protein content.
It makes a very stiff dough and I do it in the Kitchen-Aid mixer, alternatively if you do it by hand you will not need to go to the gym. It seems like a lot of work but of you have the mixer it is actually a cinch, you just need to decide the day before that you're going to do bagels.
The barley malt is the sweetener. This should be able to be replaced with another sweetener if you can't use barley.
Gluten: Gluten is a protein found in specific grains (wheat, spelt, kamut, barley, rye). Other grains are naturally gluten-free but may have cross-contact with gluten-containing grains. Look for certified gluten-free products if you need to avoid gluten. Find out more about wheat and gluten substitutions.