COMMAND

Orginal non-OO: &{\&{$testname}}($system);
updated as OO:  $self->{&{\&{$testname}}}->($system); #system is hashr
+ef
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With the updated post above, it becomes clear that BrowserUk's suggestion is correct. The code:

&{\&{$testname}}($system);
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translates to $testname->($system); with a hack to get around the ban on Symbolic references. Essentially, you have a scalar storing the name of that routine, which then calls that function with the argument $system. To change that to a method call on $self, you would want

$self->$testname($system);
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as documented in Method Names as Strings in perlobj.