A rotary drilling apparatus and method for drilling subterranean formations, including a body being provided with at least one cutter thereon exhibiting reduced, or limited, exposure to the formation, so as to control the depth-of-cut of the at least one cutter, so as to control the volume of formation material cut per rotation of the drilling apparatus, as well as to control the amount of torque experienced by the drilling apparatus and an optionally associated bottomhole assembly regardless of the effective weight-on-bit are all disclosed. The exterior of the drilling apparatus may include a plurality of blade structures carrying at least one such cutter thereon and including a sufficient amount of bearing surface area to contact the formation so as to generally distribute an additional weight applied to the drilling apparatus against the bottom of the borehole without exceeding the compressive strength of the formation rock.