Preheat oven to 425 degrees. Spray a baking sheet with cooking spray to coat (even if nonstick). Parchment paper can be used, but spray the parchment paper.
Place grated carrots in a colander and press with a paper towel to remove most of the liquid from the vegetable.
Add flour, baking powder, salt, and pepper to a bowl and stir to combine. Add beaten eggs and carrots. Stir to combine well. Let sit for 10 minutes. Form into patties (about 3 inches each) and place in rows on the baking sheet. Do not let patties touch.
Bake for 20 minutes or until crisp, flipping halfway through.
Meanwhile, whisk together all of the ingredients for the yogurt sauce and serve on the side or as topping.
*Note: if batter is too wet to form patties, sprinkle in additional flour. If too dry, add an additional beaten egg.