Best way to handle the Rossolimo Attack

Let us ask Carlsen:

https://www.chessgames.com/perl/chessgame?gid=1937779

You are out of luck. The Rossolimo is specifically played to remove all dynamic play out of Black. He has to endure the slow positional grind and show that the Bishop pair is superior.

You cannot force aggression all the time in any opening. The other aggressive defense to 1.e4 besides the Sicilian, namely the French, has lines where Black must grind it out in a slow manner, like the Exchange Variation, even though, say, the Winawer is wild, aggressive, and exciting.

Choose an open Sicilian as black with a 2...e6 system

Best is likely e6 or g6.
The real question is what are you playing 2... Nc6 for? Are you trying to reach a Sveshnikov, a Dragon, a Classical, a Four Knights, a Taimanov, or something else?
Unless the answer is that you're playing one of the Dragons, I'd recommend 3... e6, with some lines like this.