For the roux: Whisk together the Gluten-Free All-Purpose Flour (25 gram) and Water (1/2 cup) in a small saucepan - cook over medium high heat, whisking constantly, until thickened - it is ready when the whisk leaves a visible trail as it moves through the roux.
Remove from the heat & allow to cool until no longer hot to the touch.
Crush Mastiha (4 drop) with Granulated Sugar (1/2 teaspoon). Set aside.
Crack 1 Large Egg (1) and separate the egg yolk from the egg white. Set aside the egg yolk.
For the dough: Place the Gluten-Free All-Purpose Flour (3 cup), Cream of Tartar (1/4 teaspoon), Granulated Sugar (1/4 cup), Instant Dry Yeast (2 teaspoon), and Kosher Salt (1 teaspoon) in the bowl of a stand mixer and use a handheld whisk to combine.
Heat the Milk (1/2 cup) with the Ground Mahlab (1/2 teaspoon) and the mastiha & sugar mixture until milk is hot but not boiling.
Allow the milk to cool and then add the Large Egg (2), Egg Yolk, Honey (1/4 cup), Orange (1 teaspoon), and roux to the saucepan, whisking well to combine.
Add wet ingredients to the flour in the bowl of the stand mixer and mix on low speed with the dough hook until the dry ingredients are incorporated into the wet.
Slowly add in the Unsalted Butter (5 tablespoon), one piece at a time, letting each piece mix into the dough before adding the next piece.
Raise the mixer speed to high and mix for another 5 minutes. The dough will be quite sticky but relatively smooth & stretchy.
Spray a silicone spatula lightly with cooking oil spray and scrape down the sides of the bowl.
Transfer the dough to a lightly oiled bowl or proofing bucket large enough for the dough to rise to double its size, and cover with an oiled piece of plastic wrap (or the oiled top to your proofing bucket). Place the dough in the refrigerator for at least 12 hours and up to 5 days.
On baking day, line a rimmed baking sheet with unbleached parchment paper & set it aside.
Remove the dough from the refrigerator and turn it out onto a lightly floured surface - knead the dough until it is smooth.
To make braided bread, divide the dough into three equally sized pieces (you can use a scale to get them identical). Shape each piece into an 18" long rope.
Braid the three pieces together.
Once the loaf is braided, carefully transfer the braided dough, already on parchment paper, to a rimmed baking sheet.
Beat 1 Large Egg (1) with Water (1 tablespoon) to make an egg wash.
Brush the top of the dough carefully but liberally with the egg wash.
Cover the braided bread with oiled plastic wrap and allow to rise in a warm, draft-free location for 40 minutes.
Brush the loaf again with egg wash, sprinkle with Sesame Seeds (1 tablespoon) and allow to continue to rise uncovered until nearly doubled in size, about another 20 minutes.
Place the bread in the center of a cold oven and turn the heat to 350 degrees F (180 degrees C). Bake for 20 minutes,
Then turn down the oven temperature to 325 degrees F (160 degrees C) and bake until the internal temperature of the bread is 185 degrees F (85 degrees C ) on an instant-read thermometer, about another 15 minutes.
Allow the bread to cool completely before slicing, toasting & serving with butter. Slice the bread about 3/8" thick for best results.