a judge— therefore implicates Due Process as well as Sixth Amendment rights." United States v. Nelson, 277 F.3d 164, 201 (2d Cir. 2002). In turn, "Ivkir dire plays an essential role in protecting the right to trial by an impartial jury." United States v. Daugerdas, 867 F. Supp. 2d 445, 468 (S.D.N.Y.