Scrub any dirt off the young ginger. Using a mandoline, vegetable peeler or very sharp knife, cut the ginger into 1/8-inch coins (no need to peel young ginger!). Put the ginger in saucepan, cover with the water and bring to a boil. Cover and simmer at least 15 minutes, until tender. Remove the ginger with a mesh strainer or slotted spoon, reserving the water.
Add the sugar, honey and cream of tartar (if using) and pinch of salt to the reserved water, stirring over medium heat until the sugar is dissolved. Add ginger slices and cook over medium-high heat until the syrup's temperature approaches (but stays just under) 225 degrees F (about the consistency of thin honey). Add the cranberries and remove from the heat and let stand for at least an hour and up to overnight.
Transfer the ginger and cranberries with a slotted spoon to a wire rack or large mesh strainer set over a tray, letting them dry in a warm place until no longer very moist. Reserve the ginger syrup for use in drinks. Toss the dried fruit in granulated sugar, shaking off the excess sugar (which is now ginger-flavored and also worth reserving).
Crystallized ginger can be stored in an air-tight container for several months, but you'll probably gobble it up and chop it up to mix into baked goods long before then. If pieces are still too moist, they can be further dried in a 170-degree oven before storing.