Place unsalted butter in a small sauce pan over medium heat. Cook until fully melted. Set it aside and let it cool to room temperature.
Whisk together bread flour, instant yeast, and salt in a large bowl. Set aside.
In a separate bowl, whisk together 6 eggs, water, and sugar. Pour in the unsalted butter and whisk until fully combined.
Add the wet ingredients into the dry ones and stir with a wooden spoon until no dry flour remains and a uniform mass forms. This should take about 1 minute.
Cover the bowl with plastic wrap and let it rest for 10 minutes.
Holding the edge of dough with your fingertips, fold it over onto itself halfway towards the middle. Turn the bowl 45 degrees and repeat the same process. Do this 6 more times. It should be 8 times in total. Cover with plastic wrap and let it sit for 30 minutes.
Repeat folding and rising every 30 minutes three more times. After the fourth set of folds, cover it tightly with plastic wrap and place it in the fridge for 16-48 hours.
Transfer the dough onto a lightly floured surface.
Divide the dough into 6 equal pieces.
Working with one piece at a time, pat dough into a 4-inch disk. Holding the edge of the dough, fold edges of the dough onto itself halfway towards the center. Repeat folding until it forms a ball. Flip it over and move your hands in small circular motions to form it into a smooth round ball. Feel free to sprinkle it with a bit of flour if it sticks to your hands. Repeat the same process with the rest of the balls.
Cover with plastic wrap and let it rest for 5-10 minutes.
Grease two loaf pans with melted butter.
Place three brioche balls in each loaf pan. Cover loosely with plastic wrap and let it rise for 2 hours.
Thirty minutes before baking, adjust the oven rack to the middle position. Turn a baking sheet upside down and place it on the oven rack in the middle position. Preheat it to 350 degrees.
Remove plastic wrap and brush the now-risen dough with an egg. Set them on the baking sheet and bake until golden brown, rotating pans halfway through baking, 30-35 minutes or until the internal temperature reaches 190 degrees F.
Take them out of the oven and let them rest for 10 minutes on a wire rack. Being careful not to burn your hands, carefully loosen the edges with a knife. Remove them from the pan, and let them cool to room temperature on a wire rack before slicing.