Line two baking sheets with parchment. Gently deflate the dough and divide into 12 equal pieces.
Roll each piece into a tight ball and set on the sheets, spacing well.
Flatten slightly and press a deep well in the center of each bun with your fingers or a measuring cup.
Spoon 1–2 tablespoons blueberry filling into each well. Cover and let rise until puffy, 30–45 minutes. Preheat oven to 375°F.
Whisk the egg with milk. Brush the dough edges and sprinkle with coarse sugar.
Bake until golden and the filling bubbles, 18–22 minutes. Cool on a rack for 15 minutes.
Stir glaze ingredients until smooth, then drizzle over warm buns if using.