1/4 cup of shredded basil OR 1/4 cup of basil that is then shredded?

Volume measurements of herbs are hopelessly imprecise to begin with; what you actually measure as 1/4 cup depends entirely on how tightly you pack them, how wet the leaves are, even the size/shape of your measuring cup or spoon. When given a measurement like that, you should always treat it as a rough guideline; don't worry about being exact, it's not necessary in this recipe.

That said, what it actually means is that you should measure out the 1/4 cup and then shred them. Another example of this type of language is when you see something like "4 tbsp of vegetable oil, divided" - that always means you measure out the 4 tbsp and then divide into two portions, not measure out two separate portions of 4 tbsp each.

So measure it first, then shred it. If you were supposed to shred it first, it would say "1/4 cup shredded fresh basil leaves" instead. There is an appreciable difference as to how much basil you'll end up with, but again, you've been given a very rough measurement to begin with, so treat it accordingly, and don't worry if you've got a little extra or a little less. The most reliable way to know if you've got the right amount is to simply taste it.

Personally, I'd read that as measure first... shred second... There is a difference as shredded leaves will take up a lot less space than non-shredded.

But... regardless with fresh basil (and other herbs) you usually add right at the end to get maximum flavour impact (fresh herbs' flavour will diminish if cooked for long periods of time). Since this is the case, the key part in that recipe "stir in the basil and taste". Add in the roughly 1/4 cup, taste and add then more to get the impact you like.

Keep in mind that these quantities aren't even right in the book.

The original recipe called for

"Reach into the garden, and grab a medium handful of basil -- Yeah, that looks about right..."

But cookbook publishers insist on everything being a measured quantity. So very often, the end up making a precise, yet wrong quantity. This is particularly prevalent in recipes from famous chefs and restaurants. The Batali cookbook is notorious for it's screwed up quantities. You see, Mario has never made 4 servings of X in his life. He makes 25-50 servings. Now, divide that "1 head of Garlic" into a home quantity, and you'll probably be wrong.