Mix the levain by combining the ripe sourdough starter, all-purpose flour, granulated sugar, and water. Knead until a firm ball forms, then place in a covered container and let rise overnight at 78ºF for 10–12 hours, until doubled and domed.

Warm the milk to 90–100ºF. In the bowl of a stand mixer fitted with a dough hook, add the ripe levain, warmed milk, and melted butter. Add the sugar, egg, salt, lemon zest, and most of the bread flour. Mix for several minutes, adding any remaining flour as needed, until the dough is supple, tacky but not overly sticky, and cleans the sides of the bowl. Knead 8–10 minutes in the mixer (or 10–15 minutes by hand) until smooth.

Place the dough in a covered container and allow to bulk ferment at 78–80ºF for 4 hours, checking dough temperature and structure as needed. When the dough is puffy and elastic, continue; if not, extend fermentation by 30 minutes and recheck.

Once bulk fermentation finishes, cover the dough and refrigerate overnight. The next day, continue with shaping and proofing the rolls.

For the blueberry compote, combine blueberries, sugar, and lemon juice in a small saucepan over medium heat for about 5 minutes, mashing the berries as they cook. Stir in the cornstarch and cook 10–15 seconds longer, until the mixture thickens. Cool completely before using, refrigerating if making ahead.

Before shaping the rolls, remove the dough from the fridge. To make the lemon filling, mix together the softened (or melted) butter, sugar, lemon zest, and a pinch of salt into a thick paste.

Line a 9x13-inch pan with parchment or use a nonstick pan. Roll the dough into a 16x12-inch rectangle. Evenly spread the lemon filling to all edges, then gently spread the cooled blueberry compote over the lemon layer. Starting with the long side closest to you, roll up the dough tightly and pinch the seam to seal. Place seam-side down and cut into 8 equal portions. Arrange rolls snugly in the pan, with two in the center and three on each side.

Cover the baking pan and proof the rolls in an 80–85ºF area for 3–4 hours, or until the rolls have risen and puffed visibly. Do not bake until fully proofed.

Preheat the oven to 350ºF. Bake the rolls for about 30 minutes, until they are cooked through. Check the centers of a few rolls to ensure doneness, and continue baking if needed.

For the frosting, whip the softened butter and cream cheese with a hand mixer until smooth. Add powdered sugar, lemon juice, lemon zest, and a pinch of salt. Whip for 2–3 minutes, scraping the bowl as needed, until the mixture is light and fluffy.

Spread the frosting over the tops of the warm blueberry lemon sweet rolls and serve.