Add the room-temperature milk, instant yeast, and granulated sugar to a large bowl and mix together.
Add the flour, salt, softened butter, and 2 tablespoons of soaked black cake fruits. Mix until the ingredients begin to come together.
Use your hands to work the dough in the bowl, pulling it up and folding it over itself until the butter is fully incorporated and the mixture comes together into a soft dough.
Lightly grease a clean bowl. Lightly oil your hands if needed to help release the soft dough from the mixing bowl, then transfer it to the greased bowl. Cover and leave in a warm place until doubled in size, about 2 hours.
While the dough rises, combine 500 grams of soaked black cake fruits with the brown sugar. Set aside.
Once the dough has doubled, turn it out onto a lightly floured surface. Gently flatten it, then roll it into a rectangle.
Spread 4 tablespoons of softened butter evenly over the dough, followed by the black cake fruit filling.
Using a pizza cutter, cut the filled dough into 6 even strips. Roll each strip individually to form a cinnamon roll.
Lightly grease an 8×8-inch baking pan and arrange the 6 rolls inside. Cover and allow them to rest for about 15 minutes. Meanwhile, preheat the oven to 350°F.
Pour 1 tablespoon of heavy cream over each cinnamon roll.
Bake for 25 to 30 minutes, checking at 25 minutes. Make sure the dough in the center rolls is cooked through before removing the pan from the oven. Mine needed the full 30 minutes.
Remove from the oven, cover, and allow the cinnamon rolls to cool for about 15 minutes.
To make the frosting, mix the softened butter, powdered sugar, and vanilla extract until combined and smooth.
Spread the frosting over the warm cinnamon rolls to taste. You may not need all of the frosting.