In the bowl of an electric mixer fitted with a dough hook, mix the flour, yeast, sugar, and salt in a large bowl on medium/low speed. Slowly add the warm water. Stir in just enough water for your dough to form a ball and clean the bottom of the bowl.
Knead the dough on medium/low speed for roughly 10 minutes. While it is kneading slowly incorporate the extra 3/4 cup (3 ¾oz/105g) of flour until your dough is smooth and elastic. Try working in as much flour as possible to form a firm but stiff dough. Add a few drops of water if needed to incorporate more flour. (See video for a step by step)
Lightly brush a large bowl with oil and turn the dough to coat. Cover the bowl tightly with cling wrap and a dishtowel. Let rise in a warm place for 1 hour, until the dough has doubled in size.
Once doubled, punch the dough down and carefully divide the dough into 8 pieces (roughly 4oz/115g each).
Shape each piece into a smooth, round ball. Now, take a dough ball, and press it gently against the countertop moving your hand and the ball in a circular motion pulling the dough into itself while reducing the pressure on top of the dough slightly until a perfect dough ball forms. Repeat with the rest of the dough.
Gently press your finger into the center of each dough ball to form a ring. Stretch the ring to about 1/2 the diameter of the bagel (around 1 1/2 inches) and place on a lined cookie sheet. Repeat the same step with the remaining dough. Once more, repeat the process of shaping the bagels as they might have sprung back into shape. (Watch video for step by step!)
After shaping the dough rounds and placing them on the cookie sheet, cover with cling wrap and a towel and allow to rest for 20 minutes.
Meanwhile, preheat your oven to 425ºF (210ºC) and bring a large pot of water to a boil. Carefully place the bagels one by one into the water. Boil as many as you are comfortable with boiling. Let them boil there for 2 minutes, and then flip them over to boil for another 2 minutes. Boiling the bagel makes for that authentic chewy bread we love in a New York style bagel.
Remove bagels and place them back on your lined cookie sheet. Egg wash one by one and top with the ingredients listed above or add your own flavor. Bake for about 20 minutes or until golden brown.
So, bagels actually aren’t at there very best straight from the oven. Leave them in an airtight container overnight at room temperature and the flavor and texture are significantly better (you will see). Enjoy within 3 days or freeze for up to 8 weeks.