Prepare the Dough:

1. Activate the Yeast: In a small bowl, warm the milk to about 110°F (43°C). Add the sugar and yeast, stirring gently to dissolve. Let it sit for about 5-10 minutes until the mixture becomes frothy.
2. Mix the Wet Ingredients: In a large bowl, whisk together the eggs, honey (if using), and vanilla extract. Add the activated yeast mixture and stir to combine.
3. Add the Dry Ingredients: Gradually add the flour and salt to the wet ingredients, mixing until the dough starts to come together.
4. Knead the Dough: Turn the dough out onto a floured surface and knead for about 10-15 minutes, or until the dough becomes smooth and elastic. You can also use a stand mixer with a dough hook attachment on medium speed for about 8-10 minutes.
5. Incorporate the Butter: Gradually add the softened butter, one tablespoon at a time, kneading the dough until fully incorporated. The dough will be sticky at first, but continue kneading until it becomes smooth and slightly tacky to the touch.
6. First Rise: Place the dough in a lightly oiled bowl, covering it with a clean kitchen towel or plastic wrap. Let it rise for about 1 ½ to 2 hours, or until it has doubled in size.

Shape and Bake:

7. Punch Down the Dough: After the dough has risen, punch it down gently to release the air. Turn it out onto a floured surface and shape it into a loaf or divide it into smaller portions for rolls.
8. Second Rise: Place the shaped dough into a greased loaf pan (or roll portions into a baking dish). Cover and let the dough rise again for 1 hour, or until it has risen above the top of the pan.
9. Prepare the Egg Wash: Preheat your oven to 350°F (175°C). If desired, brush the top of the dough with a beaten egg to give it a glossy finish.
10. Bake: Bake in the preheated oven for 30-35 minutes, or until the bread is golden brown on top and sounds hollow when tapped on the bottom.
11. Cool: Let the brioche cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.