I am still hunting for recipes that traditionally need an oven, but have bypassed the “heat oven to 425 degrees”. The best reference has been the Mother Earth News. Here is the link for baking without an oven.
Here is a cake cooking recipe for stove top cooking that might work. It is from an interesting site. Below is just the stove top baking instructions for a cake. You have to have your own cake recipe.
Step 1: Place a rack or stand in a big heavy EMPTY pot. Make sure the pot is dry and completely clean otherwise if it has any oil or water it will smoke.
Step 2: Cover the pot with a tight lid and turn the heat on high for 5 minutes. This is to pre-heat the pot in preparation for the cake.
Step 3: Open the pot, careful it will be hot in there. Place your cake pan gently on the rack/stand.
Step 4: Cover the pot once more and let the cake start baking! First keep the heat on high for 5 minutes, then lower it to medium and continue cooking for another 20 minutes. This is for an 8″ cake size, it will take slightly more time if the cake is larger or less time if it is smaller.
Step 5: Open the pan after the baking period, and check if the cake is done. The top will be solid and a skewer inserted in the center of the cake will come out clean.
Step 6: Turn the cake over on a rack gently and remove the greaseproof paper. As you can see, the cake is done!