Whisk together flour, salt, and yeast in the bowl of stand mixer.
Add honey, vanilla extract, eggs, egg yolks, vegetable oil, and water.
Place on the stand mixer fitted with dough hook, Mix on low for 30 seconds and gradually increase to high speed. Continue to mix for about 2 minutes or until the starts to come together.
Remove from the mixing bowl and place surface covered with a little oil. Form the dough into a ball.
Place in loosely covered (I suggest lightly oiled plastic wrap) bowl and set out to rise for about two hours or until roughly doubled in size.
Punch down the dough.
If you plan to make one large loaf, divide the dough into four even pieces. If you want to make cupcake-sized challah rolls, divide the dough into 12 pieces and then divide each piece into four pieces.
Use the photos and video instruction in this post to braid the dough into a round loaf.
Set in a warm place to rise for 90 minutes.
Preheat oven to 350 F.
Brush challah with egg yolk.
Bake for 40 minutes or until the top is golden and you can see some light browning in the folds of the bread.
Set on a cooling rack to cool.