Add the warm milk, 1 teaspoon of sugar, and yeast to a small bowl and stir just until combined. Let sit for 10 minutes or until bubbly and frothy. (If the mixture doesn't bubble, your yeast is probably gone bad and you will need to start over with new yeast.)
Once bloomed, whisk the room-temperature eggs, sugar, and salt into the yeast mixture. Add 3 cups of flour and begin mixing on low speed with the hook attachment until the dough comes together.
Increase the speed to medium and gradually add the softened butter, 2 tablespoons at a time, allowing each addition of butter to incorporate before adding more. Once all the butter is incorporated, add the remaining ½ cup of flour and mix until combined. Keep mixing/kneading at medium-low speed for about 10 more minutes until a smooth and satiny dough forms.
Form the dough into a smooth ball, place it back in the bowl, and cover it with plastic wrap. Let rise in a warm place for 1 hour or until doubled in size. After 1 hour, punch down, form into a ball, cover again, and place in the refrigerator to rise/rest for 1 hour or until doubled in size.
After 1 hour in the refrigerator, punch down the dough again and transfer to a lightly floured countertop. Use a rolling pin to roll the dough into a large rectangle, approximately 12X18 inches. Spread the softened butter all over the dough, then sprinkle the sugar, lastly distribute the raspberries, pressing them into the dough slightly.
Roll the dough up tightly, starting from the long side of the rectangle. When you get to the end, pull the loose flap up over the roll and pinch the dough together to create a seam.
Prepare a baking pan with non-stick spray or parchment paper. Slice into 12 even rolls and place in the prepared pan. Cover with plastic wrap and let rise in a warm place for 45 minutes.
Preheat the oven to 350℉. Once the rolls are done rising, bake in the preheated oven for 25-35 minutes or until golden brown. Let cool slightly while you make frosting.
To make the frosting:
Whisk together the melted butter, powdered sugar, vanilla, and enough whipping cream to reach a spreadable consistency. Spread over the slightly cooled rolls and serve while still warm.
Notes
Add an additional ½ teaspoon of salt to the dough if using unsalted butter.
Store sealed tightly at room temperature for up to 3 days.