The next morning your stiff starter will have doubled. It is ready when you see lots of bubbles all around and under the jar and it has double.
Scald milk over stove top or microwave.
Slice butter and place in heated milk along with the sugar. Stir until butter is melted.
Pour milk, melted butter, and white sugar into bowl of your stand mixer. Once your milk mixture has cooled to to below 110 degrees (or is comfortable to your finger), add all of your stiff starter and blend with dough hook to incorporate starter into warm liquid.
Add egg, salt, and flour 1 cup at a time, with the mixer on low speed, until dough pulls away from bowl and is no longer sticking to the sides of the bowl, that will be about 2 3/4 cups.
Knead in a stand mixer on medium speed (or turn out on a clean surface if kneading by hand) for 5 minutes until soft and elastic.
Form dough into a ball and place dough in a greased large mixing bowl, cover with a tea towel, and let rise until double in a warm place for about 4-8 hours.
After the first rise, turn out onto your work surface and let dough rest for 10 minutes. Divide dough into three equal pieces and roll into about 14 inch logs. Place on a baking sheet prepared with a piece of parchment paper or silicone mat and form into a braid. Cover and let rise again for about 2-3 hours.
When the braid has doubled in size, brush with egg wash and bake in preheated oven at 375 degrees F for 15-20 minutes or until golden brown.