Stir together water and yeast (4 1/2 tsp = 2 pkgs) in large bowl of electric mixer; let stand 5 minutes to soften yeast. Stir in the sugar and salt. Gradually mix in 4 cups of the flour and beat at medium speed for 5 minutes. With a spoon, stir in about 1 1/4 cups more flour to make a stiff dough. Turn out on a floured board and knead until smooth, elastic, and no longer sticky, (about 15 minutes); add more flour as needed to prevent sticking - dough should be firmer than for most other yeast breads. Place in a greased bowl, cover, and let rise in a warm place until almost doubled ( about 40 minutes to 1 hour).
Punch dough down and divide into thirds. Set 2/3 of dough aside on a floured board; cover with clear plastic. Form remaining 1/3 dough in a log and cut into 16 equal pieces.
To shape, knead each piece into small ball and poke thumbs through centre. With one thumb in hole (hole should be at least 1/2 inch) work fingers around perimeter, shaping ball into a small donut- like shape about 1 1/2 inches in diameter. Place bagels on a floured board or tray and let stand 20 minutes.
Bring water-sugar mixture to a boil in a 4 to 5 quart pan; adjust heat to keep it boiling gently. Lightly grease a baking sheet and sprinkle with cornmeal. Lift bagels carefully and drop into water (about 6 at a time) boil gently for 1 minute turning only once (30 seconds each side). Lift out with slotted spoon and drain very briefly on paper towels, and place on baking sheet. Brush with 1/3 of the egg yolk glaze, sprinkle with seeds and bake in a 400° oven for 20 minutes or.
until richly browned. cool on racks.
Repeat with remaining 2/3 dough (you may need to punch it down before shaping,) working with 1/3 at a time. Makes 48 cocktail size bagels, or 12 to 18 larger bagels.