Using a garlic press, squeeze 1 tablespoon of ginger juice from the chopped or grated ginger. Alternatively, grate the ginger and squeeze the juice through a fine-mesh strainer, cheesecloth, or your hands. Transfer the juice to a heatproof serving bowl and set aside.
In a small saucepan, warm the milk over medium heat, adding about 1 tablespoon of sugar, or to taste. Heat the milk until it reaches 163 to 168°F. It will be steaming but not boiling. Remove from heat and stir briefly to fully dissolve the sugar.
Immediately pour the hot milk into the bowl, aiming directly at the ginger juice. Cover the bowl and let it sit, undisturbed, for 6 to 12 minutes.
Check if the pudding has set by giving it a gentle wobble. Then, lightly place a spoon on top. The spoon should float without sinking if the pudding is ready. Serve warm and enjoy.
