(makes a dozen large bagels)
1/2 pkg active dry yeast (1.5 teaspoons)
2 T malt syrup
2 c water, at room temperature
Stir in:
6 c bread flour (white, unbleached)
1 T salt
Mix thoroughly, then turn out the dough onto a floured surface and knead, adding enough flour (2 - 3 cups) to make a stiff dough. Knead until the dough is smooth and elastic throughout (15 minutes or so).  Then let the dough rest, covered, for 5 - 10 minutes.
Split the dough into a few pieces and roll each one into a rope of 3/4" - 1" diameter.  Form each bagel loosely around the broad part of your hand, breaking off enough dough to close the circle.  Roll the seam gently to achieve a uniform circle.  Set them to rise on a pan that is either dusted with corn meal or oiled lightly.  The center holes should be quite large at this point.  Cover them with a dry or slightly dampened dish towel and let them rise for 20-30 minutes.
Pre-heat the oven to 450 - 500 degrees.  Bring a pot of plain water to a low, simmering boil.  Slide a few bagels at a time into the water and cook for about a minute.  They should start to float within 10 seconds.  Lift them out with a slotted spoon, optionally dipping them in a topping (poppy seeds, sesame seeds, coarse salt, minced onion or garlic), and place them on a dry baking tray.  Bake for 12-15 minutes.
Notes & Variations:
  1. Homemade bagels are great, and can be made, start to finish, in under two hours, with time in-between for doing other things.
  2. Proof the yeast in a few tablespoons of warm water (not hot...body temperature is fine) to make sure it is alive.  If the yeast is good, it should start to activate in a few minutes, foaming up a bit.
  3. If you can't find malt syrup (which is made from barley), you can substitute a combination of corn syrup and brown sugar.
  4. Bread flour is higher-protein (gluten) than all-purpose flour.  Gold Medal and King Arthur brand bread flours are often available in stores.
  5. One trick to know when the dough is sufficiently kneaded is to 'pull a window': take a small piece of dough and slowly pull it apart between your hands.  It should form a translucent pane.  If it breaks apart easily, then it is not sufficiently developed.  (If you use an electric mixer with a bread hook, it is possible to over-knead the dough.)