The Savarin is relatively simple and done quickly. Just two short rising periods. Nevertheless I don't become good friends with this cake. I had to read and re-read and read again how it is assembled. Can it be you more or less just put the "filling" beside the cake? - Yes, it can.
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I had no ring-mold so I made some improvisation and used a usual spring form and put a small soufflée-form in the middle. That worked pretty well. But the dough did rise quite abit during baking and so I ended up with a too high cake. I split it in the middle, but that neither didn't look right. So I brought the two halves together again, spreading some orange jam inbetween the 'layers' to make them stick together. I am pretty convinced that my cake does not look like a Savarin at all.
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For the recipe have a look at Dorie Greenspan's book at pp 415-416.