In a large mixing bowl, combine 3 cups of all-purpose flour, 1/4 cup of sugar, and 2 teaspoons of active dry yeast. Warm 1 cup of milk to about 110°F and pour it over the mixture, adding 1 egg and a pinch of salt. Mix until a rough dough forms, then knead on a floured surface for about 10 minutes until smooth and elastic. Place it in a greased bowl, cover, and let it proof in a warm area for 1 hour or until doubled in size.

While the dough is proofing, prepare the creamy custard. In a saucepan, gently heat 2 cups of whole milk over medium-low heat. In a bowl, whisk together 4 egg yolks, 1/3 cup of sugar, 1 tablespoon of cornstarch, and 1 teaspoon of vanilla extract. Gradually pour the warm milk into the egg mixture while whisking vigorously to temper the eggs, then return the mixture to the saucepan. Cook over low heat, stirring constantly until thickened, about 5 minutes, then set aside to cool.

Once the dough has risen, punch it down and turn it out onto a lightly floured surface. Roll it out into a rectangle about 1/4 inch thick. Cut the dough into squares, approximately 4 inches on each side. Spoon a dollop of cooled custard and a teaspoon of raspberry jam into the center of each square. Fold the corners of the dough over to encase the filling, pinching to seal. Place the shaped buns on a baking sheet lined with parchment paper.

Preheat your oven to 400°F. Allow the shaped buns to rest for about 20 minutes while the oven heats. Bake the buns for 15-18 minutes, or until they turn golden brown and puffed up.

Once baked, let the Sugar Raspberry Danish Buns cool on a wire rack for about 10 minutes. If desired, mix powdered sugar with a touch of milk to create a simple glaze. Drizzle the glaze over the warm buns for an elegant touch.