Combine 1 cup of the milk and yeast and let sit until foamy, about 5 minutes.
Grease a large baking dish and set aside.
In a mixing bowl, combine the flour, egg, butter, salt, and 1/4 cup of the sugar. Pour in the milk and yeast and mix until combined. If your dough parts of your dough are still dry and not fully coming together, add the remaining 1/4 of the milk. If your dough still isn't coming together, add more milk a tablespoon at a time. It should form a single ball easily once it has enough milk.
Knead, either by hand or with a stand mixer fitted with the dough hook, until smooth and elastic, 8-10 minutes. The dough should form a cohesive mass and not stick to the sides of the bowl.
Cover the bowl with a dish towel and leave to proof for 1-1/2 hours, until doubled in size. If you prod the dough with your finger and the dimple starts to slowly fill back in, that's when it's fully proofed.
While the dough is proofing, combine the berries and cardamom in a food processor and blitz until finely chopped.
When the dough is done proofing, roll it out to a 15" x 20" rectangle. Spread with the softened butter, then sprinkle with the remaining 1/2 cup of sugar. Spoon the berry mixture onto the dough, leaving about a 1/2 inch border at the edges.
Roll the dough along the long side so you have a log, then cut into 12 equal slices. Make sure to leave about half an inch of room on the sides of each row of slices. You may need a second pan to allow for the space. Arrange the slices cut side up in your prepared baking dish. Cover with a silicon cover or plastic wrap and leave in the fridge to prove overnight, about 12 hours.
The next morning, preheat the oven to 350°F. When the oven is heated, bake the rolls for 25-30 minutes, until lightly browned. If you have an instant-read thermometer, check for an interior temperature of 190°F
Remove the rolls from the oven and allow to cool for about 10 minutes.
Meanwhile, make the frosting. Combine the softened cream cheese, jam, and powdered sugar in a bowl and mix until fully blended. Then spread the frosting over the warm rolls with a spatula.
The rolls will keep in the fridge for 2-3 days.