In a medium bowl, whisk the flour, ground ginger, ground cinnamon, kosher salt, baking soda, baking powder, ground cloves, and ground nutmeg.
In a separate bowl or the bowl of a stand mixer, whip the butter on high speed until light and fluffy. Add the dark brown sugar and molasses, followed by the buttermilk and egg, mixing on medium-high speed until well combined.
With a rubber spatula or a wooden spoon, fold the dry ingredients into the butter mixture until just combined. Do not overmix.
Cover the bowl with plastic wrap and transfer to the refrigerator to chill, at least 2 hours.
To bake, preheat the oven to 350 degrees F. Line 2 rimmed half-sheet trays with baking parchment.
Use a cookie scoop to portion the chilled dough onto the prepared trays in 1 ½-inch mounds, about 2–3 inches apart.
Bake for 13–15 minutes, or until the cakes spring back when touched.
Allow the cakes to cool on the tray for 5 minutes, then transfer to a wire rack to cool completely. Meanwhile, prepare the apple compote.