Transfer the starter to a large mixing bowl.
Add the remaining challah dough ingredients to the starter, starting with 3 cups of flour.
Mix the ingredients together using a dough hook or wooden spoon. If needed, add up to 1 more cup of flour. Knead for a few minutes until the dough feels soft and smooth.
Transfer the dough to a large, oiled bowl and cover. Let it rise for about 1 1/2 hours, until the dough is double in size.
After the dough has risen, transfer dough to a floured work surface. Divide the dough into your desired amount of strands for your braid.
Roll each portion of dough into a 15"-20" log shape.
On a large baking sheet lined with greased parchment or a silicon mat, braid the loaf.
Cover the loaf and let it rise at room temperature about 1 hour.
Toward the end of the rise time, combine the egg wash ingredients in a small bowl and preheat oven to 375°F.
Brush the dough with the egg wash and bake 30-35 minutes.