use v5.16;

package Foo {
    use Moo;
    has blah => (is => 'ro', required => 1);
    sub run { shift->new(@_) }
}

say Foo->run(blah => 42)->blah;
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Doing SUPER::new will probably work in this case, though if you call it repeatedly, you won't benefit from some of the optimizations Moo does. (Moo doesn't actually built a Foo::new sub straight away, but when Moo::new gets called, it will notice that Foo::new is missing, build an optimized constructor, install it, and goto it.)

In cases where you weren't using a class building toolkit like Moo, and Foo::new was a hand-written constructor, then you definitely wouldn't want to call SUPER::new because you'd be bypassing the class's hand-written constructor (in favour of the superclass's constructor) which might be doing important stuff.