Line a baking sheet with parchment paper.
To make the dough: In the bowl of a stand mixer fitted with the paddle attachment, add the flour, cane sugar, baking powder, and sea salt. Mix on low to for 2 to 3 rotations to combine the dry ingredients.
Using a large grater, grate the butter and add to the flour mixture. Don’t mix yet. Add the egg, 3/4 cup heavy whipping cream, lemon flavor, orange flavor, lemon zest, and mandarin zest.
Mix on low to combine until you have a shaggy dough, don't over mix as you still want to see small pieces of butter. You’ll have to scrape the bowl to help combine the dry ingredients, and I find it’s easier to finish combining with your hands.
Using your hands, form the dough into a round disk that is about 7-inches in diameter. Using a sharp knife, cut into 6 triangle pieces like a pie. Separate the pieces so they are spaced evenly apart.
In a small dish, add the 2 tablespoons heavy whipping cream for the topping. Using a pastry brush, brush the tops of the scones to coat completely.
Place the baking sheet in the fridge for 30 minutes. Preheat the oven to 400°F.
Bake for 20 to 24 minutes or until lightly golden brown on the bottoms. Allow to cool completely on the baking sheet.
To make the glaze: In a medium bowl, add the powdered sugar, lemon juice, and mandarin juice. Whisk until you have a smooth glaze.
Drizzle the glaze on top of each scone.
Store in a cool dry place for up to 3 days.