Your superfluous definition of isDefined makes the code quite hard to read, and the prototype on a method is silly since method dispatch never checks them, but here's what I fiddled it apart to, with a bit of guessing:

sub interpolateValues {
    return unless defined $INTWeb::Properties::INTERPOLATE_VALUES;

    my $self = shift;
    my $list = shift;

    my $get_value_for = sub {
        my $var = shift;
        # !!!
        # the following doesn't seem right
        # don't you need to return $list->{var}
        # if ->{Resolved}->{var} is undef?
        # that seems to be your culprit
        return $self->{Resolved}->{$var}
            if defined $list->{$var}
            or defined $self->{Resolved}->{$var};
        
        die "FATAL: $var is not a valid propery variable name\n";
    };

    while(my($key, $val) = each %$list) {
        if($val =~ s/\$\{(.*?)\}/$get_value_for->($1)/ge) {
            # ???
            # you don't seem to be storing this anywhere?
        }
        else {
            $self->{Resolved}->{$key} = $val;
            delete $list->{$key};
        }
    }
}
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Makeshifts last the longest.