Place eggs, water, vegetable oil, sugar, and salt in the bread pan. Then, place bread flour into the bread pan and spread it out to the edges of the pan. Make a little well in the middle of the flour and pour the yeast into it.
Use the dough cycle on your bread maker.
When dough cycle is finished, place the bread dough on a lightly floured surface. Divide the dough into thirds, making three 13-inch-long ropes with tapered edges. Pinch ropes together at one end and braid together. Pinch together at the other end and secure braid.
Transfer braided dough to a baking sheet lined with parchment paper; cover and let rise in a warm place for 1 hour or until doubled in size.
Combine glaze ingredients and brush onto braid. Sprinkle with poppy seeds and bake at 350 degrees F/177 degrees C for 25 minutes, or until done.