Hydrocarbon exploration and production relies on Blowout Preventers (BOPs) to prevent catastrophic accidents; however, currently there are no in-situ or rapidly deployable backup systems for BOPs. This paper presents a method and machine for predictably stemming an uncontrolled flow resulting from a failed Blowout Preventer. The tool, referred to as the "Hampering Active Wellbore Kit" (HAWK), is a machine that can feed wire (with varying material properties along its length) through a BOP's existing ports and into the wellbore. The wire, initially stored in spools inside the device, forms a tangled wire mass (TWM) inside the wellbore that serves to gradually stem the uncontrolled flow. A design theory is described for wire feeding in order to form a TWM in a free flowing conduit, and the efficacy of the method is evaluated by comparing flow rates of a single wellbore before and after the introduction of the TWM. A prototype machine for direct attachment to a BOP as a backup safety system is presented based on operating constraints and industry requirements.