In a large bowl, lightly beat the eggs. Add the plain yogurt along with the honey or preferred sweetener, and stir until the mixture is smooth and well combined.
Grate the carrots and apples. If the apples release excess liquid, drain a little before using. Add the grated carrot and apple to the bowl and mix to combine.
Stir in the oats, baking powder, cinnamon, and chopped walnuts. Mix until you obtain a uniform batter.
Lightly grease a non-stick skillet with a lid and pour in the batter. Cover and cook over very low heat for about 5 minutes, or until fully set. Remove from the heat and transfer to a plate to cool.
Pour the batter into a prepared baking pan and bake in a preheated oven at a moderate temperature for about 20 minutes, or until a toothpick inserted into the center comes out clean.
