In a bowl, combine warm water, 1 tbsp sugar, and yeast. Let sit until foamy.
Add oil to the yeast mixture.
In a separate bowl, sift in 4 cups of flour and add a pinch of salt.
In another bowl, beat the eggs and add 1/4 cup sugar.
Combine wet ingredients (yeast mixture + eggs) with the flour.
Using a stand mixer with a dough hook on low speed, mix until dough comes together.
If the dough feels too wet, add more flour a little at a time (up to about 1/2 cup).
Knead until smooth and fully incorporated.
Lightly oil a bowl, place dough inside, and cover.
Let rise until doubled in size.
Punch down the dough and transfer to a floured surface.
Divide into either: 2 medium loaves (3 strands each), or 1 large loaf (6 strands)
Roll and knead each piece into strands, then braid.
Place on a parchment-lined baking sheet, leaving space between loaves.
Cover and let rise again.
Brush with egg wash.
Bake at 350°F until golden brown.
Let cool slightly, then serve.