My dough is too brown
Yes, you can dump both sugars in together. 

This recipe is not based on the creaming method.   Instead,  the butter is melted for a chewy cookie. 
You want the butter melted,  but not browned (although that may add flavor it is not called for in this recipe).

The  chilling and resting are essential for success.   During this time the starches will hydrate, the butter will chill,  and the dough will firm. 

Your expectations from creaming method recipes do not apply, so don't worry that the dough doesn't seem exactly the same.  The color will be darker than you may be used to.   That is okay. 

See also:  What does an overnight chill do to cookie dough, that a 4 hour chill doesn&#39;t?