In a large bowl, combine the flour, sugar, salt, baking powder, ground ginger, candied ginger, and fresh ginger. With your fingers, rub the ginger into the flour to incorporate it more evenly.
Using frozen butter, grate the butter into the flour mixture.
With clean hands, work the butter into the flour until it turns into even, large crumbs. Work it quickly and only until an even crumb is achieved. You don't want to overwork it and make the butter too soft.
In a separate bowl, combine the sourdough discard, egg, blackstrap molasses, and half & half.
Whisk well until the discard smooths out and the liquid ingredients reach a smooth consistency.
Pour the liquid mixture into the flour mixture and stir minimally until nearly combined.
With clean hands, gather the dough into a ball. Use another small splash of milk if needed to bring it together.
On a cookie sheet lined with parchment paper, press the ball of scone dough into an 8" diameter disk.
Using a knife or bench press, cut the disk into 8 wedges. Gently but quickly (before the dough gets too warm) separate the wedges on the parchment paper to bake individually.
Place the cookie sheet of scones in the freezer for 20 minutes.
While the scones are chilling, preheat the oven to 400 degrees F.
Place the cookie sheet of scones in the oven for 20-25 minutes, until lightly crispy at the edges.