One simple cheat for making an ice cream base is to use instant pudding rather than making a custard. You don't have to wait for the custard to cool, so you can get that ice cream into the machine a lot faster.
Yeah, it's not completely from scratch, but it's pretty good ice cream.
I like to use French vanilla - I think it adds richer flavor to the ice cream.
Bourbon Vanilla Ice Cream
1/2 cup sugar
1 1/2 cups whole milk
1 cup cream
1 tablespoon bourbon
Combine all the ingredients in a bowl. Whisk until smooth and you can no longer feel the grittiness of the sugar in the bottom of the bowl.
You can chill the mixture in the fridge at this point, but since the milk and cream were both refrigerator-cold when you started, you can churn this right away. No waiting. Almost instant gratification.
Churn in your ice cream maker according to the manufacturer's directions. Remove from the ice cream maker and freeze until firm.