I just finished making this. Pureeing the mint leaves the syrup with tiny flecks of mint in it, which I like. I don't think you'd want to skip the straining if you did puree because the syrup with the mint puree looks really disgusting before you strain it. Even though I blanched my leaves, the syrup turned out a dark green - my mint was dark. I think it is tasty, just not very appealing to look at.
The ice bath is to keep the color from fading.
TraceyShaw, I believe the ice bath is to stop the cooking process after the mint has been blanched in boiling water, while pureeing the herb disperses the mint's flavor more quickly. I just tried this recipe and skipped the straining/ discarding solids step to drizzle on roasted peaches and whipped cream!
The mint syrup is very tasty. I am just curious as to the benefit of the ice-water bath and the puree step.
This is the only mint syrup recipe I have seen that calls for both of those steps in the mint simple syrup process. Does anyone know?