Prepare the dough

1. In a large mixing bowl, whisk the milk and sourdough starter together until smooth and fully blended. Add the sugar and egg, whisking again until evenly combined.
2. Add the flour and salt, then work in the butter using your hands or a sturdy spoon. Mix until no visible chunks of butter remain and the dough comes together into a soft mass. The butter should be very soft—if it resists when pressed, let it warm up a bit more before continuing.
3. Cover the bowl with a damp towel and let the dough rest for 30 minutes.
4. After resting, stretch and fold the dough several times until it tightens slightly. Cover and rest again for 30 minutes, then repeat the stretch-and-fold process once more.
   Optional shortcut: Knead the dough in a stand mixer with a dough hook on medium speed for about 12 minutes instead.
5. Cover the bowl and let the dough ferment at around 70°F (21°C) for 10–12 hours, or overnight, until it has nearly doubled in size. Warmer kitchens may shorten this time; cooler spaces may need a bit longer.

Shape and fill the rolls

1. Lightly flour your work surface and turn the dough out. Gently press it into a rectangle, then roll it into a 12 × 17-inch sheet using a floured rolling pin.
2. In a small bowl, combine the frozen raspberries, sugar, and cornstarch. Use a fork to crush the berries into small pieces, roughly pea-sized.
3. Spread the raspberry mixture evenly over the dough, leaving a 1-inch strip bare along one long edge. This uncovered edge helps the rolls seal properly.
4. Starting from the long side opposite the bare edge, roll the dough up into a tight log, applying gentle, even pressure. Lightly dampen the uncovered edge with water, then finish rolling and place the log seam-side down. Let it sit for a minute to secure the seal.
5. Using a sharp, non-serrated knife, slice the log into 12 equal rolls. Rinsing the knife with water between cuts helps keep the slices neat.
6. Arrange the rolls in a greased 9 × 13-inch baking dish. Cover with a damp towel and let them rise until puffed and about half again their original size, roughly 3 hours depending on room temperature. For a faster rise, place the pan near a warm oven.

Bake and finish

1. Preheat the oven to 350°F (175°C). Bake the rolls on the center rack for 30–35 minutes, until lightly golden and baked through.
2. While the rolls are in the oven, prepare the frosting. Beat the butter and cream cheese together until smooth, then mix in the lemon juice and powdered sugar until creamy and spreadable.
3. et the baked rolls cool for about 15 minutes, then spread the frosting generously over the top. Finish with lemon zest if desired, and serve warm.