Preheat the oven to 350F.

Line the bottom of two 6-inch-round cake pans with circles of parchment paper.

To make cake, combine coconut milk, applesauce and dates in a small saucepan and bring just to a simmer over medium heat.

Remove from heat, cover and let sit for 5 minutes.

Meanwhile, in a small bowl, stir together flaxseed and 3 tablespoons water.

Transfer applesauce mixture and flaxseed mixture to a food processor, add vinegar and vanilla and puree until smooth.

In a large bowl, whisk together flour, baking powder and baking soda.

Add applesauce mixture and stir until combined.

Divide batter evenly between the prepared pans, gently shaking and tapping the pans to smooth out the top.

Bake until cakes are golden brown and bounce back in the middle when touched, 20 to 25 minutes.

Let cool completely. (Cakes will shrink slightly as they cool.)

When ready to serve, make fresh berry yogurt: Combine yogurt, berries and date in a food processor and puree, scraping down sides of food processor bowl often, until smooth and spreadable.

Loosen edges of one cake with a paring knife and transfer to a plate, discarding the parchment paper.

Spread with some of the berry yogurt, top with remaining cake and spread remaining yogurt over the second. Serve immediately.

The cake will keep refrigerated in an airtight container for up to 3 days. (Suggested age: 12 months and up)