Preheat oven to 350°F and line three 9-inch springform pans with parchment paper.
In a stand mixer, beat egg whites and cream of tartar on high speed until soft peaks form.
In a separate bowl, mix egg yolks, brown sweetener, coconut oil, vanilla, and apple cider vinegar.
Add almond flour, cocoa powder, espresso, baking powder, baking soda, and chocolate chips. Mix until thick.
Gently fold in beaten egg whites in four additions, starting with 1/4 of the whites to loosen the batter.
Divide batter evenly among the three pans and bake for 30 minutes or until a toothpick comes out clean.
Let cakes cool at room temperature for one hour, then refrigerate for at least two hours.
For the raspberry jelly, heat all ingredients in a small pot until boiling, then simmer for five minutes. Chill for at least an hour.
For the frosting, beat all ingredients together until smooth.
Assemble the cake by spreading frosting on the first layer, piping a border to hold in raspberry jelly, and repeating with the second layer.
Cover the entire cake with frosting, decorate with fresh raspberries, and chill for another hour before serving.