For the bread, preheat oven to 325 degrees F. Grease one regular loaf pan (8 1/2- by 4 1/2-inch), or four mini (6- by 3-inch) with butter or cooking spray.
In a medium bowl, whisk together flour, baking powder and salt, Set aside.
In the bowl of a stand mixer (or a large bowl, using a hand mixer) set on medium speed, beat together butter, sugar and lemon zest until light and fluffy, 4 to 5 minutes.
Add eggs, one at a time, beating to combine after each addition.
Turn the mixer to low and gradually add the flour mixture and milk. Beat until just combined.
Take care not to over beat or the bread will be tough.
Remove the bowl from the mixer and, using a rubber spatula. Stir in the cranberries and chopped crystallized ginger.
Pour the batter into prepared pan(s) and level with a spatula.
Bake until a toothpick inserted in the center comes out with only a few crumbs attached, 50 to 60 minutes for regular sized pan, 25-28 minutes for mini pans. Let the bread sit in the pan for 10 minutes.
Run a knife around the outside and turn the pan upside down to release the bread. Let cool on a wire rack for 1 hour, then glaze.
For the glaze: In a medium bowl, whisk together powdered sugar, lemon juice and zest, and salt until combined. Drizzle over cooled quick bread.