Start by soaking the raisins in warm water for about 15-20 minutes. This will make them nice and plump. Drain them well before using.
In a large mixing bowl, whisk together the flour, sugar, salt, and instant yeast.
Add the warm milk, warm water, and mix until a shaggy dough forms.
Turn the dough out onto a lightly floured surface and knead for about 5-7 minutes, or until smooth and elastic.
Roll the dough out into a large rectangle (about 12x18 inches).
Spread the cold, cubed butter evenly over two-thirds of the dough.
Fold the unbuttered third of the dough over the middle third, then fold the remaining buttered third over the top, like folding a letter.
Turn the dough 90 degrees. Roll it out again into a large rectangle (about 12x18 inches).
Fold it into thirds again, like a letter. This is your first "turn." Wrap the dough in plastic wrap and chill in the refrigerator for 30 minutes.
Repeat the rolling, folding, and chilling process two more times. So, you'll roll, fold, and chill; then roll, fold, and chill again. Each time you repeat this step is known as turn. This will will result in three "turns" in total.
While the dough is chilling, make the pastry cream. In a saucepan, heat the milk over medium heat until it just begins to simmer.
In a separate bowl, whisk together the sugar, egg yolks, and cornstarch until smooth.
Slowly pour a small amount of the hot milk into the egg yolk mixture, whisking constantly. This is called tempering, and it prevents the eggs from scrambling.
Pour the tempered egg yolk mixture back into the saucepan with the remaining milk.
Cook, whisking constantly, until the cream thickens enough to coat the back of a spoon. This usually takes about 3-5 minutes.
Remove from heat and stir in the vanilla extract and 1 table spoon of butter.
Transfer the pastry cream to a bowl, cover with plastic wrap (pressing it directly onto the surface to prevent a skin from forming), and chill completely in the refrigerator.
Once the dough has completed its final chill, roll it out into a large rectangle (about 12x18 inches).
Spread the chilled pastry cream evenly over the dough, leaving a small border along one long edge.
Sprinkle the drained, plumped raisins evenly over the pastry cream.
Starting from the long edge opposite the border, tightly roll the dough into a log.
Using a sharp knife or dental floss, cut the log into 1-inch thick slices.
Place the slices, cut-side up, on a baking sheet lined with parchment paper.
Cover the Pain aux Raisins loosely with plastic wrap and let them proof in a warm place for about 1 to 1 1/2 hours, or until they are puffy and have almost doubled in size.
Preheat your oven to 375°F (190°C).
Mix one egg and 2 table spoon of milk. Gently brush the tops of the proofed Pain aux Raisins with the beaten egg wash. This will give them a beautiful golden color.
Bake for 18-22 minutes, or until golden brown and cooked through.
Let the Pain aux Raisins cool slightly on a wire rack before serving. They're best enjoyed warm, but they're also delicious at room temperature.