The huge advantage to doing a no-cook ice cream is that you don't have to wait as long for it to cool down before you churn it. If you have all the individual ingredients chilled, you could churn it immediately, particularly if your ice cream maker has a compressor.
If you've got a freezer-bowl model, you might want to give the mixture just a little refrigerator time, but an hour is probably sufficient.
Since the chocolate syrup is the main flavor in the ice cream, use one you like. I used Hershey's.
No-Cook Chocolate Ice Cream
2 cups heavy cream
1/2 cup milk
1/2 cup chocolate syrup
1 14-ounce can sweetened condensed milk
1/2 teaspoon salt
1 tablespoon vanilla extract
Whisk all of the ingredients together to combine.
If the ingredients aren't cold, refrigerate until fully chilled. Or, if you have an ice cream maker with a compressor (rather than a freezer bowl) you can churn right away.
Churn in your ice cream maker according to manufacturer's instructions.
Transfer to a storage container and freeze until firm.