Chocolate Chip Cookies - classsic or duds?

I (once again) made the Claire Saffitz cookie recipe for a little office cookie competition, and I noticed that the written recipe has you only brown half the butter, then add in the rest. But in her youtube video (which is what I wrote down my recipe from), she just throws in two sticks and browns all the butter. Clearly it's not a big deal, but I wonder how much of a difference it makes -- surely more brown butter is better? :)

I started with the Chris Morocco recipe early in the pandemic and have tried a few others, but this is currently my #1.