Preheat oven to 350 degrees F (175 degrees C). Spray baking sheet with cooking spray.

Whisk flour, oats, baking powder, baking soda, and ground cinnamon together in a bowl; stir in carrots and dried cranberries. Add dark brown sugar, light brown sugar, eggs, butter, oil, maple syrup, vanilla extract, and salt to the carrot mixture and stir until dough is well combined.

Drop tablespoonfuls of dough about 2 inches apart onto prepared baking sheet.

Bake in preheated oven until edges are brown, 12 to 15 minutes.