People who do that usually have chemical engineering degrees and very expensive equipment.
I DO have a Chemical Engineering degree, and you can’t do this at home. The biggest problem (as noted above) is that the lighter gasoline is already gone. That means you’d have to further crack the oil. Not a simple process.
The other part of the process that you’ve described is fractional distillation. This part maybe could be done at home (ask moonshiners), but not on your heating oil.