How do you get this ultra-smooth cartoonish looking effect?

You can get most of the way there with Lumetri. Make sure you have the Color workspace turned on so you can see the scopes and start at the top. Increase saturation, decrease shadows, try increasing contrast, use the Creative section to add some vibrance, maybe sharpening, saturation, and try a little split toning by warming up the highlights and cooling off the shadows. Then fiddle with curves and clean things up with controls like Hue vs. Saturation and maybe Luma vs. Saturation.  If you don't know how to read or set up scopes, use the Search Help field in AE to look up Lumetri. You will find a Premiere Pro tutorial, but the UI is almost identical, and the procedure is almost the same. 

Here's a quick example from some stock footage.