Put warm water in a large bowl and sprinkle yeast over it. Add 2 eggs, honey and oil, and mix until combined. Add flour, one cup at a time, mixing after each cup. Knead the dough with your hands until no longer sticky (about 10 minutes), adding more flour if needed. Cover the dough with plastic wrap and let rise at room temperature for 1 1/2 hours or until doubled in bulk.
Knead the dough again for 5 minutes. If the dough gets sticky, add a little more flour until no longer sticky.
Line 2 baking sheet with parchment paper.
Divide the dough into 2 equal parts. Divide each part into 3 and roll each third into a long snake. Pinch the 3 rolled parts together at the top and braid them like a braid, then pinch down the bottom to seal, making a braided challah loaf. Repeat with the second part of the dough, making the second braided loaf.
Put the two braided challah loaves on two baking sheets. Cover each with a towel or plastic wrap and let rise at room temperature for 1 more hour.
Preheat the oven to 375F.
Whisk the remaining egg and brush the challahs with the egg.
Put the challah in the oven and bake for 30 minutes.