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, salt, and lemon zest. Mix with a spatula or the dough hook on low speed until a shaggy dough forms and no dry streaks of flour remain. Cover the bowl and let it rest for 30 minutes (autolyse).

After the rest, add the softened butter cubes to the dough. If using a stand mixer, knead on medium-low speed for 8-10 minutes, until the butter is fully incorporated and the dough is smooth, elastic, and passes the windowpane test. If kneading by hand, knead for 10-15 minutes.

Transfer the dough to a lightly oiled clean bowl, turning once to coat. Cover the bowl tightly with plastic wrap or a damp towel. Perform 3-4 sets of stretch and folds every 30 minutes over the next 1.5-2 hours. After the last set, let the dough bulk ferment at room temperature (around 70-75°F / 21-24°C) for another 4-6 hours, or until it has noticeably increased in volume (about 50-75%) and is bubbly.

Once bulk fermentation is complete, gently deflate the dough, cover, and place it in the refrigerator overnight (8-12 hours) for a cold proof. This helps develop flavor and makes the dough easier to handle.

In a small saucepan, combine the raspberries, granulated sugar, and lemon juice. Cook over medium-low heat, stirring occasionally, until the raspberries break down and the mixture is simmering, about 5-7 minutes. If using frozen raspberries, they will release more liquid.

In a small bowl, whisk the cornstarch with 1 tablespoon of water to create a slurry. Stir the slurry into the raspberry mixture. Continue to cook, stirring constantly, for 1-2 minutes until the filling thickens. Remove from heat and let it cool completely before using. You can make this ahead of time and store it in the refrigerator.

Lightly grease a 9x13 inch baking dish or line it with parchment paper. Take the dough out of the refrigerator. On a lightly floured surface, gently roll the cold dough into a large rectangle, approximately 12x18 inches (30x45 cm) and about 1/4 inch thick.

Spread the cooled raspberry filling evenly over the entire surface of the dough, leaving a small border (about 1/2 inch) on one of the longer edges.

Starting from the long edge opposite the border, tightly roll the dough into a log. Pinch the seam gently to seal. Use a sharp knife or unflavored dental floss to cut the log into 12 even slices, each about 1.5 inches thick.

Arrange the cut rolls in the prepared baking dish, leaving a little space between each roll. Cover the dish loosely with plastic wrap or a damp towel and let them proof at room temperature for 2-4 hours, or until visibly puffy and almost doubled in size (the exact time will depend on your kitchen temperature and starter activity).

Preheat your oven to 375°F (190°C) during the last 30 minutes of proofing.

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

While the rolls are baking, prepare the lemon glaze. In a medium bowl, whisk together the sifted powdered sugar, fresh lemon juice, and lemon zest until smooth and pourable. Add more lemon juice a teaspoon at a time if it's too thick, or more powdered sugar if it's too thin.

Once the rolls are out of the oven, let them cool in the pan for about 10 minutes before drizzling generously with the lemon glaze. Serve warm and enjoy!