Follow these step-by-step instructions to bake your own Sweet Vanilla Brioche Loaf:

1. Prepare the Ingredients:
   • Ensure all ingredients are at room temperature for even mixing. Warm the milk slightly to activate the yeast.
2. Mix the Dry Ingredients:
   • In a large mixing bowl, combine the flour, sugar, salt, and instant yeast. Mix thoroughly to ensure an even distribution of ingredients.
3. Incorporate Wet Ingredients:
   • In a separate bowl, whisk together the eggs, warm milk, and vanilla extract. Gradually add this mixture to the dry ingredients, mixing on low speed until a dough begins to form.
4. Add Butter:
   • Gradually add the softened butter to the dough, a few tablespoons at a time, mixing continuously on medium speed. The dough should become glossy and elastic.
5. Knead the Dough:
   • Transfer the dough to a lightly floured surface and knead by hand for about 10 minutes until smooth and elastic. Alternatively, use a dough hook attachment on a stand mixer for 8 minutes.
6. First Rise:
   • Place the dough in a greased bowl, cover with plastic wrap, and let it rise in a warm place for 1 to 2 hours, or until it doubles in size.
7. Shape the Loaf:
   • Once risen, punch down the dough to release air. Shape the dough into a loaf and place it in a greased loaf pan.
8. Second Rise:
   • Cover the loaf pan with a clean towel and let the dough rise again for 1 hour, or until it has doubled in size.
9. Preheat the Oven:
   • Preheat your oven to 350°F (175°C).
10. Apply Egg Wash:
    • Brush the top of the loaf with the egg wash for a shiny, golden crust. Sprinkle pearl sugar on top if desired.
11. Bake:
    • Bake the loaf in the preheated oven for 30 to 35 minutes, or until the top is golden brown and the loaf sounds hollow when tapped.
12. Cool:
    • Remove the loaf from the oven and let it cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.