Combine oats, yogurt, eggs, chopped carrots, milk, protein powder, sugar, baking powder, cinnamon, salt, nutmeg, and ginger in a blender. Blend until batter is smooth. Fold in grated carrots.

Heat a griddle over medium-high heat; spray with cooking spray. Scoop batter onto the griddle using a 1/4 measuring cup, and cook until bubbles form and the edges are dry, 3 to 4 minutes. Flip and cook until browned on the other side, 2 to 3 minutes. Repeat with remaining batter.