Not from Genoa, but Naples: a slow-cooked sugo alla genovese mostly consists of stewed onions, with pork or beef, carrot and celery. It's generally used on pasta (ziti or paccheri).
The curious name (first mentioned in a cookery book in 1832) may be derived from the fact that the recipe was first recorded in the Loggia di Genoa in the port of Naples, as a variation on the Genoese ragú, which famously had no tomatoes in it. Others say it was invented by someone with the popular Neapolitan surname Genovese. The truth is no one knows for sure.
Image by viadelgusto