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In a large bowl mix together 1-1/2 cups flour, sugar, salt, and yeast. Gradually add egg yolk and warm water, and beat for 2 minutes at medium speed with an electric beater. Add 1/2 cup more flour and beat at high speed for 2 minutes. With a spoon, stir in enough of the remaining flour to make a soft dough. Turn dough onto a floured board. Knead for 8 to 10 minutes (add more flour if dough is too sticky). Place in an ungreased bowl. Cover, and let rise for 20 minutes (dough will not be doubled). Punch down and turn onto a floured board. Cut into about 10 pieces and roll each piece between your hands to make a rope about 8 or 9 inches long; pinch the ends together to form circles. Place on ungreased baking sheets. Cover and let rise for 20 minutes (not until doubled). In a large shallow pan boil 1-3/4 inches water. Stir in honey. Lower heat and add a few bagels at a time, being careful not to crowd them. Simmer for 7 minutes, turning bagels over halfway through cooking period. Place on a towel to cool for 5 minutes, then place on ungreased baking sheets. Bake bagels at 375 degrees F for 10 minutes. Remove from oven, brush with a mixture of egg white and cold water, sprinkle with poppyseeds if desired, and return to oven. Bake for 20 minutes longer. Cool on wire racks. Serve split and toasted.