You have Module::Test inheriting from itself.

Incorrect. Look again.

The following line is where your error is:

      my $self = Module::$t->new;
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I'm trying to understand what you are attempting to do here. You are wanting to call the constructor of some other class in some other Module:xxx namespace, and you are then blessing this into your passed classname.

This is syntactically invalid, and also breaks strict 'refs', or rather would bresk it if you specified

      my $self = ${"Module::$t"}->new;
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That's not right. It's perfectly legal (even under strict) to use interpolated strings as package names: "M::$t"->new. Your suggestion would look for a variable named $Module::Test and call new in the package or for the object contained in that variable, which is clearly not what the OP is trying to do.