We investigate the design of steep-slope metal-oxide-semiconductor field-effect transistors (MOS-FETs) exploiting monolayers of transition metal dihalides as channel materials. With respect to other previously proposed steep-slope transistors, these devices require simplified manufacturing processes, as no confinement of the 2D material is needed, nor any tunneling heterojunction or ferroelectric gate insulators, and only n-or p-type contacts are demanded. We demonstrate their operation by studying an implementation based on monolayer CrI2 through quantum transport simulations. We show that the subthermionic capabilities of the device originate from a cold-source effect, intrinsically driven by the shape of the band structure of the 2D material and robust against the effects of thermalization induced by the electron-phonon interactions. Due to the absence of a tunneling barrier when the device is switched on, current levels can be achieved that are typically out of reach for tunnel FETs. The device also exhibits excellent scaling properties, maintaining a subthermionic subthreshold swing (SS) up to channel lengths as short as 5 nm.