In the bowl of a stand mixer, add water, 1 Tbsp sugar, and yeast. Mix to combine.
In a large mixing bowl, combine sugar, flour, salt, and onion powder. Whisk to combine.
When the yeast/sugar/water is frothy, add three eggs and melted butter.
Fit the mixer with a dough hook, and turn on low/medium speed to combine all of the wet ingredients. They don't have to be perfectly combined, but the egg yolks should break and the be mostly combined.
Stop the mixer.
Add the dry ingredients in the large mixing bowl all at once.
Turn the mixer on to low speed and let the dough mix for 8-10 minutes.
After 8-10 minutes time, remove the dough from the bowl and knead by hand on a lightly floured surface for 5 more minutes. The dough may be slightly sticky. This is fine.
Return the dough back to the bowl, cover with a damp tea towel or plastic wrap, and let rise for an hour in a warm space.
Punch down the dough.
Re-cover the dough, and allow to rise another 30 minutes.
Uncover and remove the dough from the bowl.
Divide the dough into three equal pieces. You can do it by eye, or with a scale to be more precise.
Roll each of the three pieces of dough into a "log" about 20-24 inches long.
Perform a three strand plait, and place the loaf on a baking sheet. Mix together the remaining egg and 1T water.
Brush the loaf, making sure to get into the cracks of the plait, with the egg mixture. Save the remaining egg mixture and brush! We aren't done with them yet!
Preheat the oven to 375°F
Cover the loaf loosely with plastic wrap and allow to rise for another half hour while the oven preheats.
Brush the loaf with the egg mixture again.
Sprinkle liberally with Everything But The Bagel seasoning.
Bake for 35-40 minutes.
Remove loaf from oven, allow to cool for a half hour before removing from the baking sheet and moving to a cooling rack to cool completely.