How can I stop veggie garbage from coming out of my basement storm drain?
It is obvious to me that the main sewer line is restricted somewhere between the house and town line. In areas that allow storm drains to be coupled to sewer lines, it is important that these lines run freely.  If yours is backing up with kitchen waste, there is only one solution.  You need to have the line checked with a camera. you could have a simple  clog, a root growing through the line in the yard, a rust blockage if it is black pipe, etc. You won't know until it is looked at. At that point I'm sure you will need a rotary bit cleaning or a new liner installed. The longer you wait, the worse it will get.  There is no DIY cure for this type of problem.