In a medium-sized bowl, whisk together flour, baking soda, salt, cinnamon, ginger, and allspice. Set aside.
In a medium saucepan, over medium heat, melt and brown butter until it foams and gives off a nutty aroma. Set aside to cool slightly.
In the bowl of a stand mixer, fitted with a paddle attachment, add brown sugar and browned butter. Beat together for 1-2 minutes until smooth and creamy. Add egg, vanilla, and molasses, and beat until well-incorporated.
Remove bowl from stand mixer, and gradually fold in dry ingredients with a spatula. Transfer dough to a refrigerator to chill for 15 minutes. Preheat oven to 350 degrees F.
Pour 1/4 cup granulated sugar into a small bowl.
Remove chilled dough from refrigerator and use a medium-cookie scoop to scoop out equal sized portions of dough. Roll portions into balls, then roll the balls in the sugar to coat.
Place balls on a non-stick cookie sheet and bake in preheated oven for 9-10 minutes. Let cool on cookie sheet for 1 minute, then transfer to a wire rack to cool completely.
In a microwave or over a double boiler, melt white chocolate until smooth. Dip cookies into melted chocolate and top with sprinkles if desired. Place cookies on a sheet of wax paper and allow the chocolate to set up at room temperature.
