Preheat the oven to 180°C (350°F). Line a 7x7 inch square pan with parchment paper and set aside.

Lightly beat the eggs in a bowl or large pitcher until combined.

Add the honey or maple syrup and vanilla to the eggs and stir briefly.

Add the oats, baking soda, and ground cinnamon. Stir to combine.

Fold in the softened butter or coconut oil and blend until the batter is mostly smooth. A few small oat bits are fine.

Gently fold in the shredded carrots until evenly distributed.

Pour the batter into the prepared pan and smooth the top with a spatula.

Bake for 20 to 30 minutes. Check with a toothpick in the center; it should come out clean or with a few moist crumbs.

Let the cake cool in the pan for 10 minutes. Lift it out using the parchment and transfer to a wire rack to cool completely.

Serve warm or at room temperature. Top with yogurt, a light cream cheese frosting, or a drizzle of honey if you like.