Preheat the oven to 350°F. Grease an 8-inch round cake pan and line the bottom with parchment paper.

Grate the carrots on the small holes of a box grater and measure 2 tightly packed cups; set aside.

In a large mixing bowl, whisk the eggs until slightly frothy.

Add the unsweetened applesauce and vanilla bean paste to the eggs and whisk until smooth.

Add the almond flour to the bowl, then sprinkle the baking soda, baking powder, cinnamon, nutmeg, and salt evenly over the flour.

Stir until the dry ingredients are fully incorporated and the batter is smooth and thick.

Fold in the grated carrots and chopped walnuts until evenly distributed in the batter.

Pour the batter into the prepared cake pan and spread it into an even layer with a spatula.

Tap the pan lightly on the counter to release any large air bubbles.

Bake on the center rack for 50 to 60 minutes, until the top is golden, the edges are set, and a toothpick inserted into the center comes out clean or with a few moist crumbs.

Remove the pan from the oven and let the cake cool in the pan for 10 minutes.

Run a knife around the edge, turn the cake out onto a wire rack, peel off the parchment, and let it cool completely.

Slice and serve plain, or top with Greek yogurt or your favorite sugar free frosting.