App.pm

# ...
sub startup {
  my $self = shift;

    $self->hook(
        before_dispatch => sub {
            my $c = shift;
            warn $c->req->to_string;
            my $base = Mojo::URL->new(scalar $c->req->headers->header('X-Proxy-Path'));
            $c->req->url->base( $base );
        }
    );
}

# ...

nginx.conf

# ...

http {

# ...

    upstream test {
        server 127.0.0.1:3000;
    }

    server {
        listen       *:80;

        location /test {
                proxy_pass http://test/$request_uri;

                proxy_set_header X-Proxy-Path "/test";
                proxy_set_header Host $host;
                proxy_set_header X-Real-IP $remote_addr;
                proxy_set_header X-Forwarded-For $remote_addr;

                proxy_connect_timeout 120;
                proxy_send_timeout    120;
                proxy_read_timeout    180;
        }
    }
# ...
}