It may help to talk it through in words first. The pattern you're looking at is:

• Two dollar signs (metacharacters, will need escaping)
• An open parenthesis (also needs escaping)
• Some text up to a closed parenthesis (capture this in $1)
• A closed parenthesis (escaped)
• Anything else that exists beyond that (captured in $2)

Now just put those elements together in a regex:

if( $line =~ m[ \$\$     # two dollar signs
                \(       # open paren
                ([^)]+)  # capture until closed paren
                \)       # close paren
                (.*)     # capture the rest, if any
               ]x ){
   # do stuff with $1 and $2
}
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