In the large bowl of an electric mixer, beat butter, oil, and brown sugar until smooth. Add egg, applesauce, and vanilla; beat until blended. Beat in baking powder, soda, and salt, then flour, until smooth. Scrape side of bowl, then stir in oats and chocolate.
Bake dough right away; if allowed to sit, cookies will be dry. Drop dough by 2 tablespoon portions onto 2 lightly oiled 12x15 inch baking sheets, spacing evenly. Dip fingertips in granulated sugar, then pat cookies into 1/3 inch thick rounds.
Bake in a 350 degree oven until pale golden, about 10 minutes; switch pan positions after 5 minutes. Lift to racks; eat warm or cool.
Makes about 25.
Per cookie: 145 cal. (29.5% from fat) 2.3 g protein 4.6 g fat (1.9 g sat) 25 g carbo 104 mg sodium 11 mg chol