In a small bowl, combine the warm water, sugar, and active dry yeast. Stir gently and let sit for 5 to 10 minutes until foamy.
In a large mixing bowl, whisk together the flour and salt.
In a separate bowl, whisk together the eggs, egg yolk, vegetable oil, and honey.
Add the yeast mixture and the egg mixture to the flour mixture. Stir with a wooden spoon until a shaggy dough forms.
Turn the dough out onto a lightly floured surface and knead for about 10 minutes until smooth and elastic. Add small amounts of flour if the dough is too sticky.
Place the dough in a lightly oiled bowl, cover with a clean kitchen towel or plastic wrap, and let rise in a warm place for 1 to 1.5 hours, or until doubled in size.
Punch down the dough and turn it out onto a floured surface. Divide the dough into three equal portions.
Roll each portion into a long rope, about 16 inches long. Pinch the ends together and braid the three ropes tightly.
Place the braided loaf on a parchment-lined baking sheet. Cover loosely with a towel and let rise for another 45 minutes until puffy.
Preheat the oven to 350°F (175°C).
In a small bowl, whisk together the egg wash (egg yolk and 1 tablespoon water). Brush the entire loaf with the egg wash.
Sprinkle sesame seeds evenly over the top of the loaf.
Bake the challah for 25 to 30 minutes, or until golden brown and the loaf sounds hollow when tapped on the bottom.
Remove from the oven and let cool completely on a wire rack before slicing.