In a medium sauce pan combine, salt, sugar, butter, and milk. Warm over low heat to about 110 - 115 degrees.
In large electric stand mixer, combine 1 cup flour and yeast. Add your warm milk mixture and combine. Add 2 eggs, one at a time. Add vanilla and lemon zest. Mix to combine at high speed for 3 minutes.
Add 1 1/3 cup flour. Beat for 5 minutes to form a stiff dough.
Place dough in a greased bowl, cover and let rise in a warm place for about 45 minutes.
Once dough has risen, place onto a floured work surface. Punch and knead dough briefly. Form into an oval and cut into 3 even pieces. Roll out each piece into a strand around 28 inches. Repeat other two.
Place all 3 strands onto a parchment lined baking pan and pinch 3 ends together. Start braid from the closed side. Bring the open side of braid to the closed side and make a circle, closing the end together to form the cirlcle.
In between the braid openings place your colored eggs around the braid. Place one in the center. Cover braid and let rise an additional 30 minutesf.
Preheat oven to 350 degrees.
Brush egg yolk mix onto dough. (Do not brush egg yolk onto eggs)
Bake for 25-35 minutes until golden brown. Allow to cool before slicing.