Activate the Yeast: In a very large mixing bowl, combine the yeast and sugar with 2 cups of the warm water. Let this mixture sit for 15 to 20 minutes until it becomes frothy and bubbly—this indicates the yeast is active and ready to work.
Combine Wet Ingredients: Add the eggs, honey, oil, salt, and the remaining 3 cups of warm water into the yeast mixture. Stir gently to combine all the wet ingredients.
Begin Mixing the Dough: Gradually add half of the flour to the wet mixture, stirring continuously. The dough will start to come together into a thick batter-like consistency.
Incorporate Remaining Flour and Knead: Add the rest of the flour in small increments, mixing well after each addition. Continue adding flour until the dough feels soft but is no longer sticky to the touch. Once the dough reaches the right consistency, knead it for several minutes directly in the bowl or on a lightly floured surface, either by hand or with a stand mixer fitted with a dough hook.
First Rise: Cover the bowl with a damp cloth or plastic wrap and place it in a warm, draft-free spot. Allow the dough to rise until it has doubled in size, about 1½ hours.
Prepare for Braiding: Gently punch down the risen dough to release excess air. Let it rest for 10 minutes to relax the gluten, making it easier to shape.
Divide and Shape Dough: Cut the dough into six equal portions. For each portion, roll the dough into three strands and braid tightly, pinching the ends to seal. Alternatively, create challah rolls by dividing each piece into four smaller strands and rolling them into tight spirals.
Second Rise: Place the braided loaves or rolls on greased baking sheets, cover lightly, and let them rise for another 40 minutes until puffed.
Apply Egg Wash: Whisk together the egg, honey, and vanilla extract. Using a pastry brush, carefully coat the surface of each loaf or roll to achieve a shiny, golden crust after baking.
Bake to Perfection: Preheat your oven to 375°F (190°C). Bake the challah for about 45 minutes, or until the loaves are deep golden on top and sound hollow when tapped underneath.