Preheat the oven to 375º F (180º C). Line a round cake pan of about 8.66 inches (22 cm) in diameter with parchment paper.
In a big bowl, place the eggs along with the oil, sugar and vanilla extract. Mix using a whisk for 2 minutes until it is all well combined.
Mix in the yogurt and vegetable milk. Stir in the oatmeal, whole wheat flour, baking soda, salt and cinnamon and beat for 1 minute until soft.
Add in the shredded carrot and mix until fully integrated. Pour the batter into the cake pan and bake at 375º F (180º C) for 40-45 minutes aprox. until a wooden stick comes out clean when inserted.
Once ready, turn out the cake and let it cool down completely before decorating with the frosting.
Refrigerate the coconut cream (not milk) for at least 3 hours or overnight so the liquid and fat separate. We will only use the solid part.
In a pot boil some water, or heat it up in the microwave. Once boiling, add in the cashews, turn off the heat, and let them sit there for 20 minutes until soft.
Once the cashews have rested, drain them and put them in a food processor. Add in the solid part of the coconut cream, agave syrup, vanilla extract and lime and lemon juice. Process until you get a soft frosting.
Spread the frosting on top of the cake and refrigerate for at least 1 hour before serving for all the flavors to integrate.
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