Gradually mix in 4 cups of flour, beat at medium speed for 5 minutes. With spoon add 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), adding more flour as needed. Dough should be firmer than for most yeast breads. Place in a greased bowl, cover, let rise until almost doubled
(about 40 minutes). Knead dough lightly and divide into 12 equal pieces. To shape, knead each piece, forming it into a smooth ball. Holding ball with both hands, poke your thumbs through the center. With one thumb in hole, work around perimeter, shaping bagel like a doughnut 3 to 3 1/2 inches across. Place shaped bagels on lightly floured board, cover lightly and let stand in a warm place for 20 minutes. Bring the 3 quarts of water and 1 Tbsp sugar to boiling in large kettle. Adjust heat to keep it boiling gently.
Lightly grease baking sheet and sprinkle with cornmeal. Heat oven to 400 degrees. Gently lift one bagel at a time and drop into water, boil about 4 at a time, turning often, for 5 minutes. Lift out with slotted spatula, drain briefly on a towel and place on baking sheet. Brush with glaze made with 1 egg yolk and 1 Tbsp water. Bake 35 - 40 minutes, or until well browned and crusty. Cool on rack.
ONION BAGELS: Add 1/2 cup instant toasted onion to basic dough with the yeast , water and sugar in basic recipe.