Preheat your oven to 180ºC (360°F). Line a 20 cm (7.8-inch) cake mold with parchment paper or grease it lightly.
In a large bowl, combine applesauce with Greek yogurt, egg, maple syrup, vanilla extract, cinnamon, nutmeg, and a pinch of salt. Stir well until you get a smooth mixture.
Add into the wet mixture oat flour, protein powder and baking powder. Stir the ingredients together while pouring in the milk gradually. You will need 3 to 6 tablespoons, depending on the protein powder used (see notes for more details*).
Fold the grated carrots into the batter. If desired, mix in walnuts, pecans, raisins, or shredded coconut for added texture and flavor.
Transfer your protein batter to the prepared mold, then bake in hot oven for about 30 minutes. The cake is ready when a toothpick inserted into its center comes out clean.
Let the cake cool while making the frosting.