In a small bowl, combine warm water, yeast, and 1 teaspoon of sugar. Mix well and let it rest about five minutes, or until yeast has bloomed/foamed up. (if your yeast has not bloomed/foamed up by this point, your water was too warm or your yeast is dead). Set aside.
In a large mixing bowl, combine the flour, kosher salt and sugar (or honey). Mix well to combine.
Add the eggs, egg yolk, olive oil and yeast/water mixture into the dry ingredients. Stir with a dough whisk or wooden spoon to create a rough, shaggy dough.
Lightly sprinkle a clean kitchen counter or other work surface with flour and turn the dough out of the bowl. The dough will be sticky, but that's ok. Gradually knead the 1/4 cup of flour into the dough. Begin kneading the dough by pushing the dough forward with the palm of your hands, and then fold it back over itself. Give it a quarter turn between each knead. You may use the entire 1/4 cup or just short of it, weather depending.
Depending on the weather, the dough may be sticky, so add a little additional flour as you knead, until the dough is slightly smooth and supple, but still has a little tackiness left.
Lightly coat your mixing bowl in olive oil, a few tablespoons. Put the dough in the bowl and give it a little swirl around the bowl. Flip the dough over so all sides have been covered with oil.
Wrap the bowl in plastic wrap, cover in a tea towel, and let the dough rise in a warm place for 45 minutes, until the dough has doubled in size.
After 45 minutes, punch the center of the dough down. Fold and punch the dough four times, giving the dough a quarter turn between each fold and punch.
Cover the dough back up and allow it to rise another 35 minutes. (If it's hot and humid out, check your dough after 25 minutes)
Braid the dough:
Prepare a large cookie sheet with parchment paper and set aside. Preheat your oven to 350 °F
Uncover the dough and punch it down gently in the middle. Fold the dough over onto itself and then once more.
Gently tip the dough out on to a clean work surface.
Using a knife, diving the dough in half and form two balls. Divide each ball into the number of braids you want for each challah. (I make a four braided challah so I divide each ball into four equal pieces)
To create the dough strands, using your hands, flatten out a piece of dough into a rectangle (roughly 3x5 inch). Position the rectangle so the shorter sides are on the top and bottom. Roll the rectangles up into a coil, short side to short side. Repeat this until all dough pieces are rolled into coils. Cover them with plastic wrap and allow them to rest for 8 minutes. (This is a very important step, do not skip).
Uncover the dough and roll each coil out into a 7-8 inch strand. Taper the edges of each strand.
Braid your challahs and place them on the prepared cookie sheet with plenty of space between them.
Prepare the challah for baking:
Cover the challahs with plastic wrap and a tea towel. Allow them to rise in a warm place for roughly 15-20 minutes (please note, in the winter they will rise slower and in the summer they may rise very quickly, 10-15 minutes). Your challahs are fully risen with you can poke them with your finger and the imprint remains for a few moments and the dough very slowly springs back.
Brush each challah with the egg wash. Brush on a little at a time. Be sure to get into all the nooks and crannies. Wait for about 1 minute until the wash starts to dry. Apply one more coat of egg wash.
If you desire, liberally sprinkle your challahs with sesame seeds, poppy seeds, everything bagel topping, or topping of your choice.
Baking the challah and cooling:
Place the challahs in the oven for 28-32 minutes.
Your challahs are baked when they get a deep mahogany brown (don't worry, they won't dry out) and when you hear a hollow sound when you knock the bottoms of the challahs.
Carefully removed the challahs from the cookie sheet (they are delicate) and transfer to a cooling rack.
If you are planning on eating them right away, let the challahs rest for 30 minutes after baking. As tempting as it is don't eat them straight from the oven.
Notes
Water Temperature: The temperature of the water should be delicately warm enough as for a baby’s bath. Place a finger to the bottom of the cup of warm water. Keep it there a few moments. If it feels nicely warm without an “ouch” sensation, the water is the proper temperature.If you chose honey as your sweetener of choice, keep in mind it will yield a softer, slightly stickier dough. That's perfectly fine! You may need to sprinkle a little more flour on the dough when working with it.