Grate the frozen butter using a box grater. Return the butter to the freezer to stay cold while you prepare the rest of the ingredients.
In a large bowl, whisk to combine the flour, baking powder, cardamom, ginger and salt. Add the grated butter to the dry ingredients. Combine with your fingertips, two forks, or a pastry cutter until you have pea sized crumbs.
In a medium sized bowl, whisk together the sugars, lemon zest, heavy cream, egg yolk and vanilla extract.
Pour the wet ingredients over the flour-butter mixture and stir until just combined. Stir in the strawberries til just combined. Do not overmix. Dough shouldn't be dry and should be somewhat sticky but not too sticky. If there are dry spots, add a bit more heavy cream. If it's too sticky (sticking to your hands a lot), add a little more flour.
Turn the dough out onto a lightly floured surface. Lightly flour your hands. Shape the dough into a cirlce about 1 to 1 and 1/2 inches thick. Aim for a circle between 6 and 8 inches. Use a sharp knife to slice the dough into 8 triangles. In a small bowl, beat the egg. Brush the tops of the scones with the beaten egg. Sprinkle the tops with coarse sugar. Place scones on a baking sheet lined with parchement paper. Refrigerate scones 15 minutes.
Preheat oven to 375 degrees.
Bake scones 18 to 20 minutes or until edges are golden brown and the tops are lightly browned. Allow scones to cool 15 minutes on the baking sheet then top with white chocolate or icing and enjoy warm or room temperature.