To prepare pastry: Whisk all-purpose flour, whole-wheat flour, baking powder and salt in a medium bowl.

Puree cottage cheese in a food processor. Add sugar, milk, oil and vanilla and process until smooth. Add flour mixture and pulse 4 or 5 times, just until the dough clumps together. Turn out onto a lightly floured surface and gently knead several times; do not overwork. Press the dough into a disk, dust with flour and wrap in plastic wrap. Refrigerate until chilled, at least 30 minutes.

To prepare filling & bake Danish: Blend cream cheese and sugar with a food processor or an electric mixer until creamy. Blend in egg yolk, lemon zest and vanilla.

Preheat oven to 400 degrees F. Cut a piece of parchment paper or foil to fit a large baking sheet. If using foil, spray it with cooking spray. Set aside nearby.

On a lightly floured surface, roll the dough into a rectangle about 12 by 16 inches. Roll the dough back over the rolling pin and transfer it to the prepared paper (or foil). Spread the cream cheese mixture down the center of the dough, leaving a margin of 3 1/4 inches on the long sides and 1 inch at either end. Sprinkle blueberries evenly over the cream cheese mixture.

Using a sharp knife, make 3-inch-long cuts at 1-inch intervals along each side of the dough at 45 degrees angles to the filling. Trim off the top corners and fold the top end of the dough over the filling. Crisscross the angled strips over the filling to create a braided effect, tucking in the dough at the bottom end. Carefully lift the paper (or foil) at each end and transfer to the baking sheet.

Blend egg white and water with a fork in a small bowl. Brush lightly over the pastry. Bake the Danish until golden and firm, 20 to 25 minutes. Transfer to a wire rack and let cool slightly.

To prepare glaze & finish Danish: Combine confectioners' sugar and 2 teaspoons lemon juice in a small bowl. Stir until smooth. Add more lemon juice if the glaze is too thick. With a spoon, drizzle the glaze over the Danish. Slice and serve warm or at room temperature.