What does make ice cream smooth and silky?
A number of factors come together to determine the smoothness of ice cream, which is almost exclusively a product of the size of ice crystal within the finished ice cream.


How fast the mix is frozen--the faster it is frozen, the smaller the crystals
Emulsifiers or stabilizers which interfere with ice crystal growth


The amount of milkfat is actually not that important; it contributes to richness on the tongue and mouthfeel, but does not really reduce the graininess.

The single best thing you can do to ensure a smooth product is to use an ice cream maker which freezes the mix as rapidly as possible, preferably within 20 minutes at the slowest.  The slower the freeze, the larger the ice crystals grow, and when they are large enough, they will feel gritty or grainy on the tongue.

One of the best ways to help your mix freeze quickly is to chill it thoroughly in the refrigerator, over night if you can.  This will have the side benefit of improving the flavor of your ice cream.

Adding so-called stabilizers or emulsifiers which interfere with crystal formation will also help.  While some of these have scary names like xantham gum, guar gum, or agar, many come from natural sources.  The most common emulsifier of all is common egg yolks.

Making a French style ice cream, whose base is a (very thin) egg custard or creme anglais will help you get a smoother, richer texture.  Of course, it will also contribute a custardy, eggy flavor which may or may not be desirable depending on your preferences.