Preheat oven to 350 degrees F. and line a 9x13 inch baking dish with parchment paper.
Melt butter in medium saucepan and let cook/bubble until browned and golden. Remove from heat and let cool for 15 minutes.
Place browned butter and sugars into a large mixing bowl or stand mixer. Beat until combined then add eggs, molasses and vanilla, mixing until well combined. Slowly stir in all purpose flour, baking soda, salt, ginger and chocolate stars or chips. Stir until combined then transfer to prepared baking dish spreading evenly. Bake for 30-33 minutes, or until baked through. Let cool for 30-60 minutes before cutting into squares. Serve room temperature or chilled.