Sift flour, baking powder, baking soda, salt, sugar, lemon zest, and allspice together in large bowl or in the bowl of food processor.
Cut the butter into the flour mixture by hand (or whiz with food processor) until the mixture becomes a meal texture and turns a slight yellow. Pour into a large bowl.
Slice strawberries and the candied ginger. Toss into the bowl with the flour and butter mixture.
Form a well in the middle and pour in the vanilla extract and buttermilk. Stir until a dough forms and spill out onto a lightly floured work surface. Knead a few times to completely incorporate the dry ingredients into the wet. Place on a sheet of parchment paper and flatten into a disk a little more than ½ inch thick. The disk should be around 8 ½ inches in diameter. Slice into six equal triangles. Sprinkle with turbinado sugar.
Freeze for 20 minutes. Preheat the oven to 425˚F.
Transfer dough and parchment paper onto a baking sheet.
Bake for about 20 minutes or until reddish-brown on top.