In bowl of stand mixer or with electric beaters, beat brown sugar, molasses, applesauce and oil until blended. Add egg whites; beat until light and creamy, about 1 minute. Beat in half of the dry mixture; beat in remaining dry mixture just until combined. Cover and refrigerate dough, at least 45 minutes.
Place granulated sugar in a small bowl. Roll dough into 1 tbsp (15 mL) balls; roll in sugar to coat. Place 1 inch (2.5 cm) apart on parchment-paper-lined baking sheets. Use tines of fork to press each to ½-inch (1 cm) thickness.
Bake in a preheated 350°F (180°C) oven until just set in centre (they'll firm up as they cool), about 8 minutes. Let cool on pan on rack for 10 minutes; transfer to racks and let cool completely.
Tip: To spice things up, add 1/2 cup (125 mL) chopped crystallized ginger to dough before chilling.
Per cookie: 61 calories, 1 g protein, 0 g fat (0 g saturated fat), 13 g carbohydrates, 0 g fibre, 0 mg cholesterol, 36 mg sodium