Bloom yeast with warm water and a pinch of sugar in the bowl of an electric mixer until foamy, about 10 minutes.
Meanwhile, heat ⅔ cup milk and butter in a small saucepan over low heat until butter is just melted, then remove from heat and stir in sugar. Add warm milk mixture to the bloomed yeast and stir to combine.
Add 2 cups flour, salt, and cinnamon to the bowl and mix on low using the dough hook attachment until no patches of flour remain. Add 2 eggs and vanilla and stir until incorporated, scraping the sides of the bowl as necessary. Add remaining 1 ½ cups flour and stir until a smooth dough forms (dough will be slightly sticky). If the mixture feels too wet, add in more flour 1 tablespoon at a time, up to an additional ¼ cup. (If making the chocolate walnut-variation, stir in the chocolate and chopped walnuts at this time).
Transfer dough to a large, lightly greased bowl and cover tightly with plastic wrap. Allow to rise at room temperature until doubled in size, about 2 hours. Note: if it is below 70F degrees in your kitchen, try proofing the dough inside the oven with the light turned on to create a warmer environment.
Preheat oven to 350F degrees. Line a baking sheet with parchment paper.
Make the egg wash by whisking 1 egg with remaining 1 tablespoon milk in a small bowl until well combined.
Once dough is doubled in size, turn it out onto a lightly floured surface. Carefully stretch and fold all four sides in towards the center, then roll into a tight ball. Cut dough into 3 equal pieces, then gently stretch and roll each piece into a 24” strand (Note: if the dough feels tight and springs back after stretching, cover with a clean kitchen towel and let rest for 10 minutes, then proceed). Braid the strands together, then form a circle by bringing the ends together and tuck the corresponding ends into each other to create a seamless braid. Carefully transfer braided dough to prepared baking sheet, then cover with a clean kitchen towel and allow to rise for about 45 minutes, until puffy. Once dough is proofed, it should spring back slowly when poked with a lightly floured finger.
Brush dough with an even layer of egg wash. Gently tuck dyed eggs into the braid (this is a good way to hide any seams!) Top with sprinkles, if using. Bake for about 25 minutes, rotating halfway through, until bread is a golden brown and sounds hollow when you knock on it. Remove from oven and allow to cool completely before slicing and serving with softened butter. Store bread wrapped tightly in aluminum foil for up to 3 days. Tip: You can use leftover Easter Bread to make some amazing french toast!