Homemade coleslaw is the quintessential summer side to serve at a party or barbecue. Whether you like your slaw creamy or vinegary, more often than not a good slaw comes down to the cabbage slice.

Gary Oiler reached into the 15-gallon crock and grabbed two heaping fistfuls of cabbage – freshly shredded, already “stomped” – and dripping profusely. “That’s not water,” he said proudly. “That’s ...