In a stand mixer, combine warm water, instant yeast, sugar, eggs, all-purpose flour, and salt. Mix on low speed for 3-4 minutes.
Add softened butter in small pieces while mixing on low speed. Increase speed to high and mix for about 15 minutes until dough is well combined.
Let the dough rise for 1 hour at room temperature, then refrigerate for at least 2 hours, preferably 24 hours.
Shape the dough into braided loaf or brioche buns. For braided loaf, braid the dough and let it proof for 3 hours. For buns, shape and let them proof for 3 hours.
Preheat oven to 350°F (176°C). Brush the dough with egg wash and bake the braided loaf for about 45 minutes, and the buns for 20-25 minutes until golden brown.
Let the baked brioche cool on a wire rack before serving. Enjoy the feathery light and luxurious brioche with a rich buttery flavor.
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