I would copy your donut, cut down to where your bottom drip will be (straight line) separate the top surface and shell it to make it a solid. then cut the wiggly lines on it by creating boolen operation with a separate object.
Hi Chris, it's possible to use Transform >Deform > Flow to do this but it will be a bit tricky. The donut would need to be rebuilt to be just a single surface revolved from a curve with just one segment in it and the base surface would need to be a revolved plane instead of a regular 4 corner point plane.
Instead it might be easier to create some cutting surfaces to cut the donut up and shell the remaining piece to thicken it.
Loft a cutting surface between 2 curves for the outside:
Loft a similar cutting surface for the inside:
Use Edit > Trim to cut the donut with those lofted surfaces as the cutting objects.
That will make a result like this which you can thicken using Construct > Shell :
chris_donut1.jpg