Place flour, sugar, salt, and instant yeast in a large mixing bowl. In a smaller mixing bowl, add whole eggs, egg yolk, water, and butter, whisking until fully combined. Pour the egg mixture into the large mixing bowl of dry ingredients and mix to form a dough.
When the dough starts to come together, begin to hand knead for 10-12 minutes. Grease the inside of a clean mixing bowl, add the dough, and cover with a damp dish towel. Allow the dough to rest for 50-60 minutes.
Split the risen dough in half and section each half into quarters. Roll out each piece into long, even strands. Line up the four strands, pinching together at the top.
To braid the strands, follow this pattern: grab the fourth strand and gently fold over horizontally to the left across the three first strands. Grab what is now the second strand and fold over horizontally to the right across the two middle strands. Grab the first original strand, and place between strands two and three. Take strand three and fold over horizontally to the left. Take strand one, which is on the far right, and fold across between strands two and four. Lay strand two horizontally to the right across strands one and four, and strand three between one and four. Repeat this pattern until the ends of the strands. Pinch together the strands and gently fold under the braid. Repeat this with the second loaf.
Cover both loaves with egg wash. Let both loaves rise for another 50-60 minutes.
When loaves have risen, apply another layer of egg wash. Add M&B Poppy Seeds onto the first loaf, and M&B Sesame Seed onto the second. Lay both braids onto a baking sheet.
Bake the loaves at 350°F. for 30 minutes, rotating the baking sheet halfway through for even baking. Cover with foil halfway through if the bread is darkening too quickly. Let cool and slice.