Step 1: Make the Sweet Levain

1. Combine sugar, sourdough starter, milk, and flour in a bowl.
2. Let it ferment at 75°F (24°C) for 8-10 hours, until doubled or tripled.

Step 2: Prepare the Tangzhong

1. In a small pot, whisk together milk and flour over medium heat.
2. Stir continuously until it thickens to 150°F (65°C).
3. Transfer to a bowl, cover with plastic wrap touching the surface, and cool to room temp.

Step 3: Mix the Main Dough

1. In a stand mixer, combine flour, sugar, eggs, milk, levain, and tangzhong.
2. Mix until just combined, then let it rest for 30 minutes (autolyse).
3. Add salt, then knead on medium speed for 10 minutes.
4. Gradually add butter, one cube at a time, until fully incorporated.
5. Continue kneading until the dough passes the window-pane test (15-25 minutes).
6. Transfer to a lightly oiled bowl and let it proof at 75°F (24°C) for 2 hours.
7. Optional: Refrigerate overnight for an 8-12 hour cold-proof.

Step 4: Prepare the Blueberry Lemon Filling

1. Combine all ingredients in a small pot over medium heat.
2. Bring to a boil while stirring, then reduce heat and simmer for 10-20 minutes until thick and jam-like.
3. Cool completely before using.

Step 5: Shape the Babka

1. Roll out the dough into a 13×13-inch (35×35 cm) square.
2. Spread the filling evenly, leaving a ½-inch (1 cm) border.
3. Roll the dough into a tight log, then refrigerate seam-side down for 20 minutes.
4. Slice the log lengthwise into two halves, exposing the layers.
5. Twist the two halves into a braid, keeping the cut sides facing up.
6. Transfer to a buttered or parchment-lined 10-inch (25 cm) loaf pan.
7. Cover and proof for 6-8 hours at 75°F (24°C), until 80% full.

Step 6: Bake & Prepare Lemon Syrup

1. Preheat the oven to 390°F (200°C).
2. Bake for 20 minutes, then reduce heat to 350°F (175°C) and bake for another 20 minutes.
3. While baking, heat sugar, water, and lemon juice in a pot until dissolved. Let cool.
4. The babka is done when the internal temp is 203°F (95°C) and the crust is golden.
5. Brush the hot babka with lemon syrup, then let cool before slicing.