An espresso coffee dispensing machine includes a preheating boiler with temperature control, at least one hydraulic pump, and at least one dispensing assembly with systems for heating and temperature control of the water. The machine includes at least one balance for weighing the ground coffee in a filter and the dispensed product. Manual or electronic components for controlling the thermal power delivered within the preheating boiler and by the dispensing assembly are also included in the dispensing machine. The machine performs, following a rise in the temperature of the water, a pre-infusion and a post-infusion at constant pressure and for a preset volume of water calculated via a volumetric meter. Between pre-infusion and post-infusion, a brewing or infusion at constant pressure occurs wherein a presettable water volume is dispensed following calculation of the weight of the ground coffee in the filter and the product dispensed according to a brew ratio.