Preheat the oven to 350. Spray 2 large baking sheets with nonstick spray.
Combine the flour, baking powder, baking soda, and salt in a bowl; set aside. With an electric mixer on medium-high speed, beat the brown sugar, butter, and vanilla in a large bowl until blended. Beat in the sour cream and egg. With the mixer on low speed, add the flour mixture and beat until blended, about 1 minute. Stir in the oats and chocolate chips.
Drop the dough by level tablespoonfuls onto the baking sheets about 1-inch apart, making a total 36 cookies. Dip the bottom of a glass in flour and press the floured glass against each mound to make a 2 1/2-inch round. Bake, 1 sheet at a time, until lightly browned, about 12 minutes. Transfer to racks and cool. Repeat with the remaining cookies.