Preheat oven to 325F and spray a 15×10 jelly roll pan lightly with cooking spray and line with lightly oiled parchment paper.
Beat the egg yolks with 1/4 cup of the sweetener until light yellow in color and ribbons form when the beaters go through.
In a separate bowl, whip the egg whites with very clean beaters until they begin to foam, then sprinkle in the remaining 1/4 cup of sweetener and continue to beat until stiff peaks form.
Fold 1/3 of the egg whites into the egg yolk mixture to lighten it. Then gently fold in the remaining egg whites until they are almost completely combined. Be careful to retain as much air in the egg whites as possible.
Mix the Keto Chow, cocoa powder, gelatin, and baking powder together and sprinkle them over the egg mixture. Gently fold the dry ingredients into the eggs.
Using an offset spatula, spread the batter onto the prepared pan and even it out as much as possible. It’s ok if it’s a little bumpy.
Bake for 10-15 minutes until the cake is set and slightly browned around the edges but tender and soft to the touch.
Sift a layer of powdered sweetener combined with cocoa powder on a clean, dry kitchen towel. Then when the cake is cool enough to touch, carefully turn it over onto the towel and remove the pan.
Gently peel the parchment paper away from the cake and roll the cake up from the long side, using the towel with the cake rolled inside. Leave it rolled up to cool completely while you make the filling.
Whip the cream until it begins to thicken, then add the sweetener and vanilla extract. Continue to beat until stiff peaks form.
Unroll the cake and spread the raspberry jam across the inside of the cake in a thin layer. Then spread the whipped cream over the jam, leaving about 1/2 inch of plain cake around the edges. Then gently reroll the cake. Make sure not to roll the towel inside again. Wrap it in plastic wrap and chill it while you make the frosting.
For the frosting, beat the heavy cream to soft peaks and sprinkle the Chocolate Keto Chow, cocoa powder, and powdered sweetener over the top. Continue to beat until the dry ingredients are fully combined, light, and fluffy. It should be thick, but if needed, add almond milk one tablespoon at a time to thin it slightly.
Remove the cake from the fridge and unwrap it. Cut a slice from one end on a slight angle. This will be used to create a stump on the log. If you would like, you can cut a piece from the other end to create another stump. You can cut the second piece on the diagonal or straight across.
Place the cake on a board or on a serving dish and cover it with frosting. Attach the stumps you cut by pressing them into the frosting wherever you think they would look best and frost them, too. For a bark-like look, gently run the tines of a fork through the frosting along the length of the cake.
Garnish with fresh raspberries and mint leaves or anything else you would like.
Chill in the refrigerator for up to three days, or until ready to serve.