Creating amazing brioche buns is simple when you follow these steps:

1. Activate Yeast: In a small bowl, combine warm milk and sugar. Sprinkle yeast over the top and let it sit for about 5-10 minutes until frothy.
2. Mix Dry Ingredients: In a large mixing bowl, whisk together flour and salt.
3. Combine Ingredients: Add the frothy yeast mixture and eggs to the dry ingredients. Mix until a sticky dough forms.
4. Add Butter: Gradually add softened butter, one piece at a time, mixing until fully incorporated and the dough is smooth.
5. Knead the Dough: Transfer the dough to a floured surface and knead for about 10 minutes until elastic and smooth.
6. First Rise: Place the dough in a greased bowl, cover with plastic wrap, and let it rise in a warm place for about 1 hour or until doubled in size.
7. Shape the Buns: Punch down the dough and divide it into 12 equal pieces. Shape each piece into a ball and place them on a lined baking sheet, spaced apart.
8. Second Rise: Cover the shaped buns with a kitchen towel and let them rise for another 30-45 minutes until puffy.
9. Preheat Oven: While the buns are rising, preheat your oven to 375°F (190°C).
10. Egg Wash: In a small bowl, beat the additional egg and brush it over the tops of the buns for a golden finish.
11. Bake: Bake in the preheated oven for 15-20 minutes, or until golden brown.
12. Cool: Remove from the oven and let the buns cool on a wire rack for 10-15 minutes before serving.

These steps will guide you in creating the perfect brioche buns that are soft, flavorful, and simply irresistible.