This study investigated a novel continuous cold brewing method accomplished through a combined countercurrent single-screw extraction process and mechanical expression approach. The effects of four processing parameters (grind size (GS), motor rotation speed (RPM), press cone piston pressure (PCPP), and dry unbrewed coffee grounds feed rate (GFR)) on the particle size of coffee grounds, the mass balance of coffee grounds and water/brew in the brewer, and the physicochemical quality (total dissolved solids (TDS), extraction yield (EY), titratable acidity (TA), total polyphenols (TPP), pH, caffeine and 5-caffeoylquinic (5-CQA) concentration) of the brew were evaluated. The processing parameters significantly affected the mechanical interactions between the coffee grounds and brewer, resulting in changes in the packing density of coffee grounds, the moisture content of the spent coffee grounds, the extent of grind size reduction, and the amount of fines in the brew. These changes affected the physicochemical quality of the resultant brew leading to significant differences in TA, TPP, and 5-CQA, which were positively correlated with TDS.