Method for preparing a very hot beverage in a container by a beverage dispensing machine comprising a control circuit, a hot water and/or steam generator and a rotary stirring device comprising a rotary tool about an axis A and intended to cooperate with a beverage contained in the container, said rotary stirring device comprising a delivery conduit for delivering hot water and/or steam to the rotary tool, the method comprising the steps of: a) placing the container on a support, below the rotary stirring device then placing the rotary tool into said container, b) selecting and initiating a preparation with a very hot water base by the control circuit, c) injecting a volume V of hot water through the hot water and/or steam delivery conduit, after the step c), a step d) consisting of: d) injecting steam through the delivery conduit to bring the water to a temperature above 80°C, then during step d), a step d1) consisting of: d1) operating the rotary tool to stir the preparation and break the bubbles that are formed in the preparation under the action of the steam and thus prevent splashing out of the container, the method being characterized in that the beverage made comprises an ingredient to be infused that can be introduced into the container in the step a) or after the step c), and in that the method comprises at the end of step c), a step c1) consisting of: c1) operating the rotary tool during the infusion of the ingredient, the container comprising a basket for receiving the ingredient to be infused, in particular tea leaves. a) placing the container on a support, below the rotary stirring device then placing the rotary tool into said container, b) selecting and initiating a preparation with a very hot water base by the control circuit, c) injecting a volume V of hot water through the hot water and/or steam delivery conduit, d) injecting steam through the delivery conduit to bring the water to a temperature above 80°C, then during step d), a step d1) consisting of: d1) operating the rotary tool to stir the preparation and break the bubbles that are formed in the preparation under the action of the steam and thus prevent splashing out of the container, the method being characterized in that the beverage made comprises an ingredient to be infused that can be introduced into the container in the step a) or after the step c), and in that the method comprises at the end of step c), a step c1) consisting of: c1) operating the rotary tool during the infusion of the ingredient, the container comprising a basket for receiving the ingredient to be infused, in particular tea leaves. d1) operating the rotary tool to stir the preparation and break the bubbles that are formed in the preparation under the action of the steam and thus prevent splashing out of the container, the method being characterized in that the beverage made comprises an ingredient to be infused that can be introduced into the container in the step a) or after the step c), and in that the method comprises at the end of step c), a step c1) consisting of: c1) operating the rotary tool during the infusion of the ingredient, the container comprising a basket for receiving the ingredient to be infused, in particular tea leaves.