In a large mixing bowl, combine 4 cups of all-purpose flour, ½ cup of sugar, and 2 teaspoons of active dry yeast. Cut in 1 cup of cold butter until the mixture resembles coarse crumbs. Gradually add 1 cup of lukewarm milk and 2 beaten eggs, mixing until a soft dough forms. Knead gently for about 5 minutes.

Transfer the dough to a lightly floured surface and knead gently for around 5 minutes until smooth and slightly elastic. Place the kneaded dough in a greased bowl, cover it with a damp cloth, and let it rise in a warm area for about 1 hour, or until it has doubled in size.

In a saucepan over medium heat, whisk together 2 cups of milk, ½ cup of sugar, 3 tablespoons of cornstarch, 3 tablespoons of butter, and 1 teaspoon of vanilla extract. Stir continuously until the mixture thickens, about 5 minutes, then remove from heat.

Allow the custard to cool for about 15-20 minutes before using it.

Once the dough has risen, punch it down gently and roll it out on a floured surface into a rectangle approximately ½ inch thick. Cut the dough into squares, and place a spoonful of custard in the center of each square, topping with a teaspoon of raspberry jam. Fold the corners of each square towards the center to form a bun shape, pinching seams together to seal.

Arrange the shaped buns on a baking sheet lined with parchment paper. Cover the buns with a clean kitchen towel and let them rise for an additional 30-45 minutes in a warm spot until puffed and slightly larger.

Preheat your oven to 375°F (190°C). Once the buns have puffed up, place them in the preheated oven and bake for 18-20 minutes, or until they are golden brown.

Remove the freshly baked Sugar Raspberry Danish Buns from the oven, allowing them to cool on a wire rack for about 10 minutes. Serve warm.