In a medium saucepan, heat the whole milk over medium heat. If using a vanilla bean, split it and scrape the seeds into the milk, adding the bean pod as well. Stir occasionally and bring the milk just to a simmer. Once heated, remove from the heat and discard the vanilla bean pod (if used), or add the vanilla extract if using that.
In a separate bowl, whisk together the egg yolks, sugar, and cornstarch until smooth and well combined.
Gradually pour a little of the hot milk into the egg yolk mixture while whisking constantly to temper the eggs (this prevents them from scrambling). Once the egg mixture is warmed, slowly pour it back into the saucepan with the remaining milk, whisking continuously.
Place the saucepan back on the heat and cook the mixture over medium heat, whisking constantly, until it thickens and comes to a gentle boil. This should take about 3-5 minutes. Once thickened, remove from the heat.
Stir in the unsalted butter and caramel sauce until fully combined and smooth. Add a pinch of salt to balance the sweetness.
Pour the caramel pastry cream into a clean bowl, cover with plastic wrap directly on the surface to prevent a skin from forming, and let it cool to room temperature. Once cooled, refrigerate for at least 1 hour before using as a filling for the cruffins.
In a stand mixer fitted with the dough hook, combine the milk, yeast, and sugar. Mix until dissolved. Add the egg and flour, and mix on medium speed until the dough comes together. Add the salt, then gradually incorporate the butter, a few pieces at a time, until fully absorbed. Increase the speed to high and knead for 6 minutes, or until the dough pulls away from the sides of the bowl.
Transfer the dough to a lightly greased bowl, cover, and let rise until doubled in size, about 1 to 1½ hours. For enhanced flavor and texture, refrigerate the dough overnight.
An hour before rolling, remove the butter from the fridge to soften.
On a floured surface, roll the dough into a thin rectangle. Spread with softened butter, then fold the dough into thirds (like a letter). Rotate the dough, roll out again, and repeat the butter-and-fold process. Chill the folded dough in the freezer for 10 minutes.
Roll the dough into a thin rectangle. Use a pizza cutter to slice it into 4 cm (about 1.5-inch) strips. Roll each strip into a spiral and place it in a greased muffin tin.
Cover and let the dough rise for 40 minutes, until puffy.
Preheat the oven to 350°F (180°C). Bake the cruffins for 25 to 30 minutes, or until golden brown and crisp.
While still warm, roll the cruffins in sugar. Let cool, then fill with your desired filling using a piping bag.