In a large mixing bowl or the bowl of a stand mixer, combine the active sourdough starter, warm milk, granulated sugar, and egg. Mix until well combined.

Add the all-purpose flour and salt. Mix on low speed (or by hand) until a shaggy dough forms and no dry streaks of flour remain. Cover the bowl and let rest for 30 minutes (autolyse).

After resting, add the softened unsalted butter. Knead the dough on medium-low speed for 8-10 minutes (or by hand for 10-15 minutes) until the dough is smooth, elastic, and passes the windowpane test.

Transfer the dough to a lightly oiled bowl, turning once to coat. Cover tightly with plastic wrap or a damp towel.

**Bulk Fermentation (First Rise)**: Let the dough ferment at room temperature (68-72°F / 20-22°C) for 8-12 hours, or until it has noticeably increased in volume (about 50-75% larger), is bubbly, and passes the "poke test" (a lightly floured finger leaves an indentation that slowly springs back). The exact time will depend on your starter's activity and ambient temperature. Alternatively, you can place it in the refrigerator for a cold bulk ferment for 18-24 hours for a slower rise and more complex flavor.

Lightly grease a 9x13 inch baking dish.

**Prepare the Filling**: In a medium bowl, gently combine the raspberries, granulated sugar, all-purpose flour, and lemon zest. Set aside.

On a lightly floured surface, gently deflate the fermented dough and roll it out into a large rectangle, approximately 12x18 inches (30x45 cm).

Brush the melted butter evenly over the rolled-out dough, leaving a small border (about 1/2 inch) along one of the long edges.

Evenly spread the raspberry lemon filling over the buttered dough, avoiding the unbuttered edge.

Starting from the long edge opposite the unbuttered border, carefully roll the dough into a tight log. Pinch the seam gently to seal.

Using a sharp knife or unflavored dental floss, cut the log into 12 equal rolls, about 1.5 inches thick.

Arrange the rolls in the prepared baking dish, leaving a little space between each roll as they will expand.

Cover the baking dish loosely with plastic wrap or a clean kitchen towel.

**Warm Proof**: Let the rolls proof at room temperature for 2-4 hours, or until they look visibly puffy and have nearly doubled in size. They should feel light and airy. The exact time depends on your kitchen temperature.

**Cold Proof (Overnight Option)**: For a slower proof and convenience, you can cover the rolls and refrigerate them overnight for 8-12 hours. If cold proofing, remove them from the fridge 1-2 hours before baking to allow them to warm up slightly and finish proofing.

Preheat your oven to 375°F (190°C) about 30 minutes before baking.

Bake the rolls for 25-30 minutes, or until golden brown on top and the filling is bubbly. If they start browning too quickly, you can loosely tent them with aluminum foil.

Remove from the oven and let cool slightly in the pan on a wire rack while you prepare the glaze.

In a small bowl, whisk together the powdered sugar and fresh lemon juice until smooth.

Add milk or water, a teaspoon at a time, until you reach your desired consistency (it should be thick but pourable).

Drizzle or spread the glaze generously over the warm (but not hot) rolls.