Blur silhouette of mesh with material or post processing??

I am attempting to create a material or pp material that will effectively blur the silhouette of a mesh. I need to be able to detect edges and then blur inward. I would use this mask as an alpha to blend between postprocessing0 and the mesh render itself.

I know that I can create an outline with a pp material and flag meshes I want to inherit the outline as “render custom depth.” But how would I then blur inwards?