In a large mixing bowl, beat the butter and sugar together with a hand mixer until smooth and creamy. Add in the molasses and egg, then beat again until everything’s fully mixed.
Sprinkle in the ginger, cinnamon, salt, baking soda, and 1 cup of the flour. Beat until the flour disappears into the dough, then mix in the second cup. Continue slowly adding the remaining flour until the dough comes together.
Cover the bowl with plastic wrap and pop it in the fridge for 30 minutes to chill. When you’re ready to bake, preheat the oven to 350°F and line a large baking sheet with parchment paper. Roll the dough into 1½-inch balls and space them out about 2 inches apart on the tray.
Use your thumb or knuckle to press a small well into the center of each dough ball. Stir the cranberry sauce in a bowl until it’s nice and smooth, then spoon a small amount into each well—just enough to fill the space without overflowing.
Bake for 12–13 minutes. Let them sit on the baking sheet for 10 minutes, then melt the white chocolate in the microwave. Transfer it to a zip-top bag, snip the corner, and drizzle it over the tops of the cookies. Let them finish cooling on a wire rack.