Preheat your oven to 350 degrees.
In a medium bowl, whisk together the flour, baking soda, sea salt, ground cinnamon, and ground ginger. Set aside.
In the bowl of an electric mixer, beat the room-temperature butter, brown sugar, and granulated sugar until light and fluffy.
Scrape down the sides of the bowl, then mix in the egg, molasses, vanilla extract, orange extract, and orange zest until well combined.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Measure 65 gram portions of dough and roll them into dough balls. Place them at least 2 ½ inches apart on a parchment-lined baking sheet to allow for spreading.
Bake the cookies for 12 minutes, just until set. Avoid overbaking; they will continue to cook slightly as they cool.
As soon as the cookies come out of the oven, use the back of a spoon to gently nudge the edges toward the center, creating a slight lip to hold the icing and maintaining a circular shape.
Let the cookies cool completely before adding the orange glaze.