In medium mixing bowl, add warm milk, water, and melted butter. The mixture should be warm to the touch but not hot, otherwise it may kill your yeast. Mix in sugar and yeast. Let sit for 5 - 10 minutes until frothy. If you don't see any activity, your yeast could be dead. Throw out and try again with fresh yeast.
Add flour, salt, and egg to the liquid ingredients. Use a stand mixer fitted with a dough hook to knead on medium-low speed for 10 - 15 minutes. Periodically check and see if the dough is smooth and passes the window pane test, indicating that gluten has developed enough. You can also knead by hand if preferred.
Cover the dough and let rise for 60 - 90 minutes until doubled in size.
To make the filling, mix together the butter, cinnamon, brown sugar, and raspberry jam with a fork until a smooth paste forms. Set aside until the dough finishes rising.
Once the dough has doubled in size, turn it out onto a lightly floured surface. Knead a few times to release air bubbles. Roll into out into a 14 x 10 inch rectangle. Spread the surface evenly with the filling. Take one end of the dough and roll, stopping when you reach the middle of the dough. Then, take the other end of the dough and roll until the middle so the two coils are touching. Cut into 11 - 12 rolls.
Take each roll and pinch the bottom to form a pointed heart shape. Arrange in the baking dish.
Let rise for 20 minutes. While the rolls rise, preheat the oven to 375°F
Bake the rolls for 25 - 30 minutes until they're golden brown and make a hollow noise when tapped.
Make the frosting - in a small bowl, mix together the powdered sugar, vanilla, milk, and jam. If it's too thick, add a little more milk. Drizzle or spread over the freshly baked rolls.