In a stand mixer, add the flour, salt, yeast and sugar.
Add the eggs, milk and vanilla extract and mix together just until the flour is incorporated, the dough will be quite tough and lumpy at this point, this is normal.
Using the dough hook attachment for your mixer begin adding the pieces of butter as the dough turns in the bowl.
Continue until all of the butter is incorporated into the dough.
Continue until the dough is very smooth and elastic.
Do not add additional flour.
Cover and let rest and rise until double in volume.
Turn the dough out into a lightly floured breadboard and knead for about 5 minutes before forming the dough into 16 individual balls.
Roll out the individual dough balls to a half inch thickness and place one of the chocolate pieces on each portion of dough.
Bring the edges of the dough together and pinch together to seal.
Turn the petit pains over onto a silicone pad lined baking sheet so that the seams are on the bottom.
Remember to leave adequate room for the petit pains to rise and expand.
Cover with a tea towel and allow to rise at room temperature for about an hour.
When ready to bake, pre-heat oven to 350°F.
Bake for about 25 – 30 minutes until golden brown.
Cool on a wire rack for 15 minutes before serving warm.