Measure warm water into a glass measuring cup or bowl. Stir in yeast and sugar, allow to stand for 10 minutes – it should get very bubbly.
In a large mixing bowl, combine flour and salt. Pour in yeast mixture, stir well to combine.
Dump dough out onto a floured surface, knead until soft and elastic, 5-10 minutes. Alternatively, use a stand mixer with a dough hook for about 7 minutes, or until dough is smooth and elastic.
Once dough is fully kneaded, place in a greased bowl, cover with plastic wrap, and allow to rise for one hour, or until doubled in size.
Once dough has doubled, punch it down, and divide it out. We divided the mixture into 6 equally sized balls, for LARGE bagels – but you can make them smaller by dividing into 8 or 12 equal sized pieces.
Preheat oven to 350F. Line a baking sheet with parchment paper, and bring a large pot of water to a boil, while you form the bagels.
There are two main ways of forming bagels – with roll each lump of dough into a thick “snake” and secure the ends together, or roll each lump into a smooth ball before poking a finger though. Once you have a hole made, stretch the ring of dough out a bit to enlarge the hole. Personally, I prefer the latter.
Once you have all of your bagels formed, set them on a baking sheet to rise for another 10 minutes.
Turn heat down a little, allowing water to simmer rather than boil. 2 or 3 at a time, drop your bagels into the simmering water, allow to cook for 1 minute, then flip each and allow to cook for another minute. Drain well, place on a lined baking sheet.
Whisk egg together with 1 tablespoon of water, brush over the tops and sides of each bagel. Bake for 35-37 minutes (small) or 40-45 mins (large), until golden brown.