Place 1 cup of water, eggs, salt, sugar, bread flour, and yeast into the pan of a bread machine in the order recommended by the manufacturer. Select the Dough setting, and start the machine.
When cycle is completed, remove dough from the machine, and set onto a floured work surface for 15 minutes to rest. Cover dough with a towel or large bowl to prevent drying out.
Knead the dough several times, and cut into 6 equal pieces. Roll each piece out into a rope about 10 inches long and 1 inch in diameter.
Line a baking sheet with parchment paper. Lay 3 ropes of bread onto the prepared baking sheet, and pinch ropes together firmly at the ends to form a pointed triangle. Weave 3 more ropes over and underneath each point of the first triangle to make a second, interwoven triangle. Pinch it closed tightly at the edges to make a 6-pointed star. Set the baking sheet in a warm place, and allow to rise until doubled, 30 to 45 minutes.
Preheat the oven to 375 degrees F (190 degrees C). Whisk egg yolk with 1 tablespoon of water, and brush the mixture over the loaf; sprinkle with sesame seeds.
Bake in the preheated oven until the challah is shiny, golden brown, and sounds hollow when tapped, about 35 minutes.