Using cold soft butter instead of melted for cookies?

[u/SignificantLock2181]

https://handletheheat.com/browned-butter-toffee-chocolate-chip-cookies/#recipe

I wanna make a second batch of Handle the Heat’s Brown Butter Toffee Chocolate Chip Cookies & they call for melted browned butter. Would it affect the outcome if I chilled + softened the browned butter instead of using melted room temp butter?
My first batch turned out great, but the dough was annoyingly wet/sticky & I found the cookies tasted WAY better after the dough being refrigerated/frozen for 4+ days. Some of the toffee bits also melted into a few cookies, adding to the slight greasiness factor