To prepare crust: Whisk whole-wheat flour, all-purpose flour, baking powder and salt in a medium bowl. Puree cottage cheese in a food processor. Add oil, milk and sugar; process until smooth. Add the dry ingredients and pulse 4 to 5 times, just until the dough clumps together. Turn out onto a lightly floured surface and knead several times, but do not overwork. Press the dough into a disk, dust with flour and wrap in plastic wrap. Refrigerate for at least 20 minutes.

Meanwhile, prepare filling: Heat oil in a large nonstick skillet over medium-low heat. Add leeks and cook, stirring often, until tender, 3 to 5 minutes. (Add water, if necessary, to prevent scorching.) Add mushrooms and increase heat to medium-high; cook, stirring occasionally, until the mushrooms are tender and the liquid has evaporated, 3 to 4 minutes. Let cool.

Whisk egg, sour cream, salt and pepper in a large bowl. Add scallions, parsley and the mushroom mixture; toss to coat.

To assemble & bake galette: Preheat oven to 400 degrees F. Coat a baking sheet with cooking spray.

On a lightly floured surface, roll dough into a rough 15-inch circle about 1/4 inch thick. Roll it back over the rolling pin and transfer to the prepared baking sheet. Spread the filling over the dough, leaving a 2-inch border all around. Fold the border up and over the filling to form a rim, pleating as necessary. Brush egg glaze over the rim.

Bake the galette until the crust is golden, 25 to 35 minutes. Let cool on the baking sheet on a wire rack for 5 minutes. Slide onto a serving platter and serve hot or at room temperature.

Tip: To clean leeks: Trim off fuzzy root and dark green stems. With a sharp knife, cut several incisions in the leek's stem end to open it up like a fan. Soak in water for several minutes, then swish to dislodge dirt. Repeat until no grit remains.

MAKE AHEAD TIP: Refrigerate for up to 2 days. Reheat on a baking sheet at 350 degrees F for 20 to 25 minutes.