In a large mixing bowl, combine the flour, sugar, and salt.
In another bowl, dissolve the yeast in the warm milk. Let it sit for about 5 minutes until frothy.
Add the yeast mixture, melted butter, eggs, and vanilla extract to the dry ingredients. Mix until a dough forms.
Knead the dough on a floured surface for about 10 minutes until smooth and elastic.
Place the dough in a greased bowl, cover, and let it rise in a warm place for about 1 hour or until doubled in size.
Preheat the oven to 350°F (175°C).
Divide the dough into three equal parts. Roll each part into a long rope. Braid the ropes together and form into a circle, pinching the ends to seal.
Place the braided dough on a baking sheet. Gently tuck the dyed eggs into the braid, spacing them evenly.
Bake for 25-30 minutes or until golden brown. Let cool before serving.