At Knowle Cottage, we had two veggie plots, one which we managed traditionally and the other that other than keeping weed free and thinning as needed was pretty much left to its own devices.
This plot was edged by herbs in big pots with broken crock at the bottom to stop them over-spreading. Sage, varieties of mint, varieties of thyme and many others will grow happily for several years if kept weed free and trimmed back in the autumn.
Other vegetables will harvest for years with a similarly low level of attention.
Some varieties of onion come again and again, as do chives and garlic chives. Horseradish, mushrooms, artichokes, and asparagus are all multi-year croppers and rhubarb is reliable for making sweets and desserts and jam.
Leave a few carrots in the ground and the seeds will drop and produce carrots the following year. Small cherry tomatoes will also re-seed readily just from shoving one in a pot, not truly year on year but very simple to do in just a few seconds.
As you get older gardening gets harder and Edith and I love that we can still pick produce even though we put little effort in these days. We don’t have artichokes, not something we like that much, to be honest, but there’s nothing like a nice rhubarb pie after lunch and fresh horseradish sauce with a decent cut of beef.