If you’re looking to change up your summer ice cream fix from the typical, albeit iconic Mister Softee, Mr. P’s Homemade Ice Cream in Crown Heights ought to do the trick.

In cities like Los Angeles, artisan trucks such Coolhaus serve small-batch ice cream with inventive flavors. Even in New Jersey, where Mr. Softee is headquartered, there are new players.

When that familiar jingle echoes down your street, there’s no mistaking it — the ice cream truck is coming. In New Jersey, most people picture a Mister Softee truck, its grinning cone mascot ...