This was the first recipe I made in my new ice cream maker. It was delicious. One problem: there was a blob of basil leaves frozen to the paddl...

I haven't made the recipe, but I'm about to. I think your mistake was that the recipe said to remove the basil leaves from the heated mixture. There is additional fresh basil that she says to slice thinly and add to the mixture before you put it in the ice cream maker. Yet, when you look at the picture of the sherbet, the basil looks more like confetti. So it's probably better to slice the leaves into thin strips, cut the strips crosswise into little pieces of "confetti," and then add the "confetti" to the chilled sherbet base (even though the recipe doesn't say this specifically).

This can happen anytime you stir something into an ice cream or sorbet base ~ herbs, zest, etc. I just scrape them off the dasher and stir them in. Alternatively, you can wait till the mixture starts to freeze and increase in viscosity before you add the mix-in. The increased density of the mix will help it stay in suspension. Glad you like the recipe. :)

That happened to me once too, and I think I stirred them back in, As boulangere says, though -- not the end of the world if you didn't!

Perhaps, but it's probably not the end of anything if you didn't. Think about the physics of how the dasher functions. Regardless of how fine you had chopped the leaves, some number of them would have wound up wrapped around the dasher.