Preheat oven to 350°F and line a baking sheet with parchment paper.
Pulse rolled oats in a blender or food processor until they resemble coarse flour.
Finely grate the carrot and measure out one packed cup.
Combine grated carrot, oat flour, and unsweetened applesauce in a bowl. Stir until a soft dough forms. If too wet, add a little more oats; if too dry, add a tiny bit more applesauce.
Scoop small portions and flatten into bite-size rounds, or roll dough and cut into shapes.
Place treats on prepared baking sheet and bake for 18-22 minutes until firm and lightly golden.
Let treats cool completely on a wire rack before serving or storing.