For such an occasion, I use a semi-low carb cake recipe of my grandma. I do think it is more low carb than typical cakes, and it is tasty, although it is definitely not a phase 1 thing to eat!

100 g is about 4 oz.

Mix 6 egg yolks with 200 g sugar - I used Splenda, but you might risk trying fructose if you are on SB - it is lower glycemic index than real sugar - but don't try anything that doesn't have volume (like saccarin).
Then add 2 Table spoons bread crumbs, 200 g ground hazelnuts or ground almonds, a shot of rum. Beat the 6 egg whites until stiff, and slowly fold them under the mix. Don't mix thoroughly. Bake at fairly low temperature (around 340 F) for 30-45 min.

When its done for a kid's party, I add chocolate icing on one half.