Mix 1 1/2 cups flour, 3 Tbs sugar, 1 Tbs salt and yeast.
Heat 1 1/2 cups water and margarine to 120-130 degrees. Add to dry ingredients; beat 2 minutes at medium speed. Add 1/2 cup flour; beat at high speed 2 minutes. Stir in more flour to make a stiff dough. On floured board, knead 8-10 minutes. Set in greased bowl; turn to grease top. Cover; let rise in warm, draft-free place 1 hour.
Punch dough down. Cover; let rest 15 minutes. In a large skillet heat 1-inch water over medium low heat to a simmer; add remaining sugar and salt.
Divide dough into 12 pieces; shape 3 pieces into smooth balls. With floured finger, poke a 1-inch hole in each. Drop bagels into simmering water. Cook 3 minutes. Turn and cook 2 minutes. Turn again; cook 1 minute more. Drain on towels. Repeat shaping and cooking rest of dough.
Place on greased baking sheet. Mix egg white and 1 Tbs water; brush on bagels. Sprinkle with coarse salt, sesame, caraway or poppy seed if desired. Bake at 375 degrees for 20-25 minutes. Remove from sheets. Cool.