Whisk together the Gluten-Free All-Purpose Flour (3 tablespoon) and Water (1/2 cup) in a small saucepan over medium heat, whisking constantly until the mixture has thickened. Remove from the heat & allow to cool until no longer hot.
While the roux cools, add Granulated Sugar (1/2 cup), Salt (1/2 teaspoon), and Unsalted Butter (4 tablespoon) to a small dish.
Heat the Milk (3/4 cup) in a small saucepan until it is very hot, but not boiling & then pour over the butter, sugar and salt mixture, stir until the butter melts, reserve.
Add Gluten-Free Pastry Flour (3 cup), Cream of Tartar (1/4 teaspoon), and Instant Dry Yeast (2 teaspoon) to the bowl of a stand mixer and use a handheld whisk to combine.
Add the milk, sugar, butter mixture, Large Egg (2) and the roux and mix on low speed with the beater attachment until the ingredients are well combined. Raise the mixer to medium and mix for about 5 minutes.
Transfer the dough to a lightly greased bowl large enough for the dough to rise double its size. Set in a warm, draft free location until doubled, about 1 hour.
Once dough is risen, when you are ready to bake from refrigerated dough, grease an 8" baking pan, punch down the dough and on a floured work surface, divide the dough into 8 pieces.
Shape into rounds by first flattening the piece of dough into a disk.
Pull the edges toward the center of the dish, securing the edges together by pressing between your thumb and forefinger. Turn the dough over so that the gathered edges are on the bottom and coax the roll into a round shape.
Place each roll into the prepared baking pan as you go, when you are finished with all the rolls, cover with a damp towel or greased plastic wrap and allow to rise in a warm, draft free location until almost doubled, about 30 minutes for same day dough.
Preheat oven to 350 degrees F (180 degrees C).
Beat the Egg (1) to make an egg wash. Uncover the rolls, brush with egg wash and bake on the center rack of the oven for 20 minutes.
Remove from the oven and place baking pan on a wire rack to cool for about 10 minutes before serving. Enjoy with Butter (to taste)!