Preheat oven to 350 F. Line insulated baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking soda, salt, ginger, cinnamon and allspice. Set aside.
In mixer on low speed, combine both sugars and butter for 15-20 seconds. Increase speed to medium-high and beat until light and fluffy. Add eggs, one at a time, beating well after each addition. Add molasses and beat until well combined, batter will look smooth and silky. Gradually add in the flour mixture to form a fairly stiff dough.
Using a cookie scoop, place 1-inch balls on prepared baking sheets, about 1 1/2 inches apart. Bake for 10-11 minutes for soft cookies, 13-14 for crisp.
Remove from oven, cookies will appear puffed, but will settle as they cool. Leave on baking sheets for 4-5 minutes then transfer to cooling racks to cool completely.