This is what I want to achieve as my end result. In the picture (from blender) above, a 3D noise texture is passed through a color ramp and added to the roughness of the voronoi noise texture.
Your question is too abstract to give you a better answer. In general, when you need to blur a texture you should always pre-compute it whenever humanly possible. If it needs to be done in realtime, then the most efficient approach is to do it in multiple passes with a separable filter and/or downsampling depending on the size of the kernel.
For textures specifically you can usually get away with just biasing the mip level, since mipmaps are auto-generated on import. This is how unreal handles blurry reflections on rough surfaces when using reflection captures.
If you’d like, I can try to recreate the math calculations for Blender’s Voronoi noise “texture” in UE materials. This process can take some time, so to speed it up, you could also explain which Voronoi noise parameters in Blender you don’t intend to change (e.g., Dimension will always be 3D/4D, distance metrics will always be Euclidean, etc.). Then I’ll try to do it if you still need it.