In a small saucepan, combine butter and milk over low heat. Heat just until butter is melted and mixture reaches between 110-115 degrees. Remove from heat and stir in 1 tablespoon of sugar. Sprinkle on the yeast and let sit for 5-10 minutes to allow the yeast to proof.
In a stand mixer, mix together the eggs, remaining sugar, vanilla, and salt. Add in the milk/yeast mixture along with half of the flour. With the dough hook attachment, continue mixing and adding the remaining flour, until a smooth dough appears. (You may need to add more or less of the total amount of flour listed). Continue kneading with the dough hook for about 4 minutes.
Shape the dough into a ball and place in a clean large bowl. Cover with a towel or plastic wrap, and place in a warm area to rise for about an hour. (While the bread rises, you can make the dyed eggs, if using, following the instructions on the dye package).
Once the dough has risen, preheat oven to 350 degrees and line two baking sheets with parchment paper; set aside. Remove the dough from the bowl and place on a clean dry surface.
Divide the dough into 12 equal pieces. Roll each piece into 12-inch long ropes. Take two of the ropes and pinch together the ends. Cross the ropes over each other to form a twist. Pinch together the ends and connect with other ends to form a ring. Repeat with remaining dough. Place three dough rings on each lined baking sheet.
In a small bowl, whisk together one egg and a tablespoon of water. Use a pastry brush to brush the egg wash on to the dough rings. Top with sprinkles. Nestle the dyed eggs in the middle of the dough rings.
Bake in a preheated oven for about 20-25 minutes, or until the top of the bread is golden brown. Remove from oven and let cool before serving.
Lemon zest: there are many different variations of Pane di Pasqua, some which include citrus zest. If you wanted a lemon flavor, simply add the zest of a lemon along with the vanilla in the recipe.
Flour: the amount of flour you use will vary and can be anywhere from 4 cups to 5 cups. Use enough flour to make a soft, slightly sticky, ball of dough.
Large bread rings: Instead of making six small rings, you could divide the dough in half and made two large rings. Nestle the eggs within the dough ring and bake for about 10-15 minutes longer.
Decorative eggs: the dyed eggs will cook in the oven, so there is no need to boil them ahead of time.
Storage: you can leave the bread in an airtight container on the counter for up to three days. Note, that if you do this, you will have to discard the dyed eggs or store them separately in the refrigerator.