Pain au chocolat, sometimes called a chocolatine, is a doughy puff pastry made with chocolate in its center. The pastry is quite similar to a typical croissant, aside from the extra chocolate bonus.
Stir together your milk and yeast, and add your sugar, eggs and vanilla, mixing thoroughly. Toss in a cup of flour and all the salt, and then gradually add the rest of your flour as it naturally incorporates with the rest. Knead your dough and transfer it to a baking sheet. Drape it in plastic wrap and chill it for 30 minutes. Using an electric mixer, beat your butter and flour together until smooth, and then place it aside.
After your dough chills, place it on a floury surface and roll it into a large ¼” rectangle. Spread the butter over the rightmost 2/3 of the rectangle and then fold over the leftmost 1/3. Then cover that with the right side so that it lines up. Once again, cover the dough with your plastic wrap and cool it for 30 minutes in your fridge. This procedure is called a turn; perform four total turns, letting the dough chill for 30 minutes each time. After your fourth turn, refrigerate the dough overnight.
Preheat your oven to 400 degrees Fahrenheit. Roll out the dough to ¼” thickness and cut the dough into small rectangles, approximately the size of a business card or a little larger. Put a chunk of chocolate near the middle of each pastry and roll the sides up to form your croissant shape. Put them on a baking sheet and bake until they golden, which should take about 15 minutes.