Trim the crusts from the bread and flatten slices with a rolling pin.
Spread about 1 tablespoon of lemon curd on each bread slice. Line up 4 or 5 blueberries (depending on berry size) on the outside edge, and roll bread to the opposite end.
Whisk eggs and milk together in a bowl and coat each roll in the egg mixture.
Heat butter in a skillet over medium heat, and place the roll-ups seam side-down in the skillet. Cook the rolls on all sides until golden brown, 6 to 8 minutes.
Remove roll-ups from the skillet, and dust with confectioners' sugar. Serve warm.