Brewing espresso coffee (EC) is considered a craft and, by some, even an art. Therefore, in this study, we systematically investigated the influence of coffee grinding, water flow rate, and temperature on the extraction kinetics of representative EC components, employing a central composite experimental design. The extraction kinetics of trigonelline, caffeine, 5-caffeoylquinic acid (5-CQA), and Total Dissolved Solids (TDS) were determined by collecting and analyzing ten consecutive fractions during the EC brewing process. From the extraction kinetics, the component masses in the cup were calculated for Ristretto, Espresso, and Espresso Lungo. The analysis of the studied parameters revealed that flow rate had the strongest effect on the component mass in the cup. The intensity of the flow rate influence was more pronounced at finer grindings and higher water temperatures. Overall, the observed influences were minor compared to changes resulting from differences in total extracted EC mass.