Warm the milk in the microwave for 15-30 seconds. It should be lukewarm and not too hot.
Add the yeast and sugar to the warm milk and let sit for a few minutes.
Add the milk and sugar with the dissolved yeast to the bowl of a stand mixer fitted with a dough hook attachment.
Add the softened butter, eggs, salt, and vanilla extract. Whisk until mostly smooth. Don't worry if there are some clumps of butter still.
Add in 4 cups of flour and turn the mixer on low. Turn to high and add flour, 2 tablespoons at a time as needed. I added an additional ½ cup. The dough should be sticky but not so sticky that it sticks to your fingers.
Form the dough into a ball and transfer to a large bowl that has been greased with butter. Cover with a damp kitchen towel and let rise until doubled in size. About 1 hour.
Once the dough has doubled in size, punch it down and divide it into 3 equal pieces. Use your hands to roll each piece into a long skinny rope. Crimp them together at one end and place on a baking sheet covered with parchment paper.
Braid the dough like you would braid hair. Alternate crossing each end over the center rope and placing in the middle. See the post above for a visual step-by-step guide.
Cover with plastic wrap and allow to rise again for 1 hour.
Preheat oven to 400°F.
Brush the top of the dough with beaten egg yolk.
Bake in the preheated oven for 15 minutes, until golden brown and firm on the outside.
Brush the top with melted butter and serve warm with butter or jam. Leftovers last covered at room temperature for 1 week.