Mix warm water, oil and egg together into a stand mixer bowl. Mix, with kneading hook, until blended.
Add salt, sugar, and yeast and flour ( small amount at a time). Mix with hook until a soft dough is formed. You may need to add a bit more warm water ( or more flour if needed). Check the dough, it should be soft and slightly sticky. It should easily form into a smooth ball. When the right consistency is reached, knead with hook for 6 minutes.
Take dough ball out and place into oiled bowl-turn it over so that the oil in on all sides. Cover with saran wrap and let rise until doubled ( about 30 minutes or more).
Punch down dough and divide into thirds. Roll each piece into a strand . Prepare cookie sheet with parchment paper. Place all three strands onto sheet and braid. Cover with saran wrap and let rise again until doubled ( about 30 minutes or more). In the mean time preheat oven to 375°F.
Brush top of braid with beaten egg yolk and bake for 15-20 minutes or until golden brown.