In a mixing bowl, combine warm milk, yeast, and a pinch of sugar. Let sit for 5–10 minutes until foamy.
- Add flour, sugar, salt, eggs, softened butter, vanilla, and citrus zest. Knead until dough is soft and elastic, about 8–10 minutes.
- Cover and let rise in a warm place for 1–2 hours until doubled in size.
- Prepare filling: In a saucepan, cook berries with citrus juice and sugar over medium heat until berries release juices. Stir cornstarch with water, add to pan, and cook until thickened. Cool completely.
- Roll out dough into a large rectangle. Spread cooled berry filling evenly.
- Roll dough tightly into a log, slice lengthwise, and twist the halves with cut sides facing up.
- Place twisted dough into a greased loaf pan. Cover and let rise 30–45 minutes.
- Preheat oven to 350°F (175°C). Bake for 35–40 minutes until golden and cooked through.
- Cool slightly. Whisk powdered sugar with citrus juice to make glaze and drizzle over babka, if desired.