For the Dough
In a small sauce pan, warm milk and butter together until butter melts. Don't let mixture get hot. Remove from heat; add vanilla extract.
In bowl of stand mixer or mixing bowl, with paddle attachment, beat together yeast, salt, sugar and eggs until combined.
To the egg mixture, slowly add 3½ cups of the flour (set aside the remaining cup of flour) and the milk mixture (alternating) and continue to beat with paddle attachment until smooth.
Switch to dough hook attachment and knead the dough (or knead by hand on surface) until dough starts to become less sticky. Add 1 tablespoon of flour at a time until dough leaves the side of the bowl and begins hugging the dough hook. Note: you may not need to use up the remaining cup of flour.After several minutes, pull the dough with two fingers to test the elasticity. You should be able to stretch to where it creates a "window" that you can almost see through. Once the dough is soft and stretchy, place in greased bowl, cover with a thick towel and let rise for two hours until dough is double in size. If you're going to peek at the dough, make sure you stretch plastic wrap over the top of the bowl to avoid a draft.
Punch dough down on floured surface and cut into two or three equal pieces (depending on how many loaves you want). Shape into balls, cover with clean tea towel and let rise another hour, until about double in size.
Punch dough balls down and cut each ball into two or three pieces. For each dough ball, roll 2-3 long strands out, about 18 inches long, and then braid or twist, making sure to pinch both ends. Shape as preferred, place on baking sheet lined with parchment paper and cover with tea towel to let rise another 30 minutes (or so).
Heat oven to 350° F.
Before baking, tuck the colored eggs into folds as you desire. Brush tops of dough with egg wash.
Bake for about 25 minutes until tops are golden brown.