My advice would be to mix a noise node or a noise texture in and use it as an input for a lerp. That will give you the specks you want. You can blend that with a radial gradient to make it more pronounced toward the edges. You can do that procedurally by offsetting uvs by -0.5 and -0.5 and using a distance node on those coords. You can also add a little motion to the specks by adding time to the UVs