In a large bowl sprinkle the yeast over the milk. Let sit for about 5 minutes. Add the egg, sugar, salt and vanilla. Whisk gently to combine. Set aside.
Quarter each stick of butter and cut into 9 or 10 pieces. Toss the diced butter and flour together in a medium bowl.
(Optional method) Put the flour in the bowl of a food processor. Cut each stick of butter into 1/4 inch slices and mix into the flour. Pulse machine 8 to 10 times, just to cut the pieces of butter into 1/2 inch pieces. If there are any larger pieces, break them with your fingers.
Add the flour and butter mixture to the wet ingredients and fold with a rubber spatula until the flour is completely moistened. Transfer the dough to a smaller bowl, cover with plastic wrap and refrigerate overnight.
Remove the dough from the refrigerator. On a heavily floured surface, pat it into a rectangle about 8 x 6 inches, and then roll it into a larger rectangle about 14 x 24 inches. Brush off any excess flour and fold both edges in so that they meet in the center. If the dough is sticking underneath, release it with a long flexible metal palate knife. Dusting off any excess flour and fold the dough in half when the edges meet. This is called a "book or 4-fold". Rotate the rectangle of dough 1/4 turn on the table. This is called a "turn". Roll into a rectangle measuring about 24 x 12 inches, loosening the dough underneath with a the metal spatula, reflouring as necessary. Brush off any excess flour and give it another book fold. Wrap the dough in plastic and refrigerate for 20 to 30 minutes.
Remove the dough from the fridge and repeat this process two more times, rolling the dough out each time to 12 x 24 inches. There are 4 book folds in all. After the final turn, shape the package into a rectangle measuring about 9 x 6 inches. Brush off any excess flour, wrap in plastic and refrigerate for up to 2 days or freeze for up to one month.