Rimmed soaps are the reason why I started soap making. I adore them.
So far I have made three and the results were mixed, but with soap you get better the more you learn.
If I may share my "knowledge":
for the rim:
make a basic soap, no fragrance, no additives (other than color), castor oil is a must, it makes it more bendable.
In my first soap I made this recipe
you pour a thin layer and then you need to get it to gel. I put mine in the oven, 50° C for 30 mins. You need to watch it. Do not overheat and dont leave it too long.
Then you have to wait for it to cool.
Then you need to cut it. The aim (for me) is to be at 4 mm. Tricky, very tricky. I have a wire which has a cork on each side and you try to slice the thin layer off.
That is the hardest part.
Cut it into the size you need. For that you roll it on the outside of the can for the first cut and then some more cutting to get to the size you need.
Then you put it inside the roll, I usually take a pringles can. You softly press it. Again a thin line between putting too much pressure and breaking it.
Once you have done this, you're as good as finished.
Make a batter for the inside, what ever pleases you, add fragrance.
Close the roll or pringles can on the bottom and pour the batter into the inside.
I think some gel it here again, but I've never done this, I think its not necessary.
Take out and enjoy!
Here is a picture of my first one
and here my so far favourite one, it had a wonderful fragrance: water lilly. The soap itself was very bubbly and I loved everything about it.
I also tried to do it with a square form, didnt have enough rim left over. And on one I experimented with gold mica oil droppings, but must say I dont really like that (it bleeds endlessly)