Wash the ginger and grate it very finely (I don`t peel it, but you can of course do that too).
In the meantime, heat the milk until it almost boils (on the stove or in the microwave). Remove from heat and stir in the ginger. Let cool down to drinking temperature (depending on the amount of ginger juice, the milk will be a little creamy). Pour into a cup (possibly through a tea strainer) and sweeten with honey as desired. Serve immediately.