In a small bowl, combine 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 flour and salt.
In a separate bowl, beat 2 eggs with vegetable oil and honey.
Add the yeast mixture and egg mixture to the flour mixture. Stir with a wooden spoon or dough hook until a rough dough forms.
Turn the dough onto a floured surface and knead for about 8 to 10 minutes until smooth and elastic. Add flour as needed to prevent sticking, but keep the dough slightly tacky.
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 about 1 to 1.5 hours, or until doubled in size.
Punch down the dough and turn it out onto a lightly floured surface. Divide the dough into three equal pieces.
Roll each piece into a long rope about 12 to 14 inches long.
Braid the three ropes together by placing the right rope over the center rope, then the left rope over the new center rope, repeating until the braid is complete. Pinch the ends together and tuck them underneath the loaf.
Place the braided loaf on a parchment-lined baking sheet. Cover loosely with a towel and let rise for another 30 to 45 minutes until puffy.
Preheat the oven to 350°F (175°C).
In a small bowl, beat the remaining egg and brush it gently over the loaf to create a shiny crust.
Bake the challah bread for 25 to 30 minutes, or until the loaf is golden brown and sounds hollow when tapped on the bottom.
Remove from the oven and let cool on a wire rack before slicing.