Make Sponge: Combine yeast and water in a bowl with a fork until yeast is completely dissolved. Add flour and stir until completely smooth and no lumps remain, about 2 minutes. Set aside until foaming and bubbly, about 20 minutes.

Make Dough: While the Sponge is developing, combine the flour and salt in a large mixing bowl. In a separate bowl, whisk together water, eggs, egg yolks, sugar, and honey until well incorporated. Once the Sponge is ready, add Sponge, liquid ingredients, and melted shortening to the flour mixture; stir until a shaggy dough forms. Use your hands to press the dough together and once it comes together into one solid mass, turn out onto a clean work surface. Knead for 10 minutes by hand until dough is supple, smooth, and very elastic. (Note: if using the dough hook on a stand mixer, knead on low speed for 6 minutes and then on high speed for 7 minutes.)

Place dough in a lightly greased bowl and turn the dough to lightly coat in oil. Cover with plastic wrap and leave at room temperature until doubled in size, about 1 hour.

Turn dough out onto work surface and divide into 4 equal pieces. Shape each piece into an oblong shape roughly 2 1/2 inches wide and 5 inches long. Spray pieces with cooking spray, cover with plastic wrap, and rest for 20 minutes.

Use the palm of your hands to press any air out of each piece of dough. Working with one piece at a time, start at the center of the dough and gently roll each piece outward into a 24-inch rope, applying more pressure with your palms as you roll closer to the edges to make tapered ends. Repeat with remaining oblong dough pieces.

Place ropes vertically parallel to each other. Starting at the center of the rope on the far right, lift the rope over the one directly next to it, then weave the rope under the next rope (the second from the left), then weave over the rope on the far left. You should now have one weave in the dough with the four tapered ends still pointing toward you in a new order. Repeat weaving process by weaving the new rope on the far right over the next rope, under the second rope, and over the far left rope. Continue weaving process until there is no more rope to weave. Press the ends together with the palm of your hand and tuck the pressed dough under itself to create a rounded and braided end.

Move to the other end of the loaf and repeat braiding process by working right to left in the same way you did in Step 6 until the entire loaf is braided. Press that end together with your palm and tuck the pressed dough under itself to create the other rounded braided end. Transfer braid to a parchment paper-lined baking sheet.

Make Egg Wash: Whisk together egg yolks and water for Egg Wash. Generously brush entire surface with Egg Wash, reserving and refrigerating remaining Egg Wash for later use. Cover braid with plastic wrap and let rise at room temperature for 1 hour.

Preheat oven to 375°F. Remove plastic wrap, brush again with Egg Wash and sprinkle evenly with sesame seeds. Bake until the outside is a deep brown and the internal temperature reaches 195°F, rotating halfway through baking, 22 to 25 minutes. Allow loaf to cool completely before slicing.