Activate the yeast: In a small bowl, mix the warm water (120°F/49°C) with 2 teaspoons of sugar and stir in the active dry yeast. Let it sit for 5-10 minutes until frothy and activated.

Mix dry ingredients: In a large mixing bowl, whisk together 4 cups of flour, granulated sugar, and salt.

Add wet ingredients: Add the eggs to the dry mixture and mix until well incorporated. Slowly pour in the yeast mixture.

Incorporate the butter: Gradually add the softened butter to the dough, a few pieces at a time, mixing continuously until fully incorporated.

Knead the dough: Add the remaining ¾ cup of flour and knead the dough on a lightly floured surface or in a stand mixer for about 10 minutes, until the dough becomes smooth, soft, and slightly sticky.

First rise: Place the dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm place for 1-2 hours, or until doubled in size.

Shape the dough: Punch down the dough and turn it out onto a floured surface. Divide and shape it into your desired loaf or roll shapes. Place them into greased pans.

Second rise: Cover the shaped dough with a cloth and let it rise again for 1 hour, or until doubled in size.

Preheat oven: Preheat the oven to 375°F (190°C).

Bake: Brush the tops of the loaves with the dissolved sugar-water mixture for a shiny finish. Bake the brioche for 25-30 minutes, or until golden brown and the internal temperature reaches 190°F (88°C).

Cool and enjoy: Remove the brioche from the oven and let it cool on a wire rack before slicing and serving.