In large mixing bowl, (or stand mixer with dough hook), stir yeast into water to soften for five minutes. Add three eggs, sugar, oil and salt. Beat lightly. Add flour in small increments, continuing to mix, until you have a smooth, moist, elastic dough.
Turn dough out onto lightly floured surface and knead by hand for five more minutes.
Put dough into a large bowl oiled with EVOO, turn once to coat entire ball of dough with oil. Cover and let rise until doubled, about 1 hour.
Turn dough out onto lightly oiled work surface. Divide into thirds. Shape each third into a rope about 20 inches long. Lay ropes side by side on baking sheet lined with parchment paper. Braid ropes, tucking both ends under loaf.
Cover and let rise in warm area 45 minutes.
Beat reserved egg with 1 Tbsp cold water to make an egg glaze. Brush glaze lightly over braid.
Bake in preheated 3507°F oven 40-45 minutes, checking with instant read thermometer (internal temperature of 190°F).