Here's everything I know about melting ice cream aside from the taste.
A procedural solution would be to mix a Magic Texture and a Noise Texture for the noisy mask, and use a Wave Texture with a high Distortion value for the outside melted part.
If you just add these masks together, however, you'll get these jagged peaks on the outside, which is not desirable.
Instead we want to Subtract the wave mask from the noise mask first, and then Add the result to the wave mask.
This will generate us some nice smooth curvature with noise on the inside.
I messed with some ColorRamps, but I couldn't get anything that I was super pleased with. The core principles are here, though. I used the same map to drive the roughness.