1. Preheat oven to 425 degrees. In a large nonstick skillet, heat oil over medium-high. Add onion; cook, stirring occasionally, until golden brown, 5 to 6 minutes. Add mushrooms; cook, stirring occasionally, until mushrooms are tender, 4 to 5 minutes. Season with salt and pepper; set aside.

2. On a lightly floured work surface, roll out dough (still folded in thirds) to a 20-by-10-inch rectangle. Using a pizza cutter or sharp knife, trim edges straight; cut dough into four 10-by-5-inch rectangles. Dividing evenly, mound mushroom mixture on one half of each rectangle, leaving a 1/2-inch border on three sides. Lightly brush border with water; fold other half of pastry over filling, and press edges firmly to seal. With a floured fork, crimp edges.

3. Using a wide metal spatula, transfer turnovers to a large baking sheet. With a paring knife, cut 3 to 4 small slits in the top of each turnover. Bake until golden and puffed, 20 to 25 minutes. Let cool 5 minutes; serve turnovers with sour cream.