In a medium bowl, combine sugar and lemon zest. Using your fingertips, mix together. Stir in flour, baking powder, baking soda, and salt.
Using largest holes on a box grater, grate frozen butter. Add to flour mixture and mix until it resembles coarse meal.
In a small bowl, combine egg and cream and mix well. Pour into flour mixture. Mix well, scraping down the sides of the bowl. Scrape dough out onto a lightly floured surface. Using hands, shape dough into a ball, making sure to fold in all the loose clumps.
Shape into a 7 inch circle, approximately 3/4 inch thick, and cut into 8 equal pieces. With space between each triangle, place on a parchment covered baking sheet. (Alternatively, you can use a scone pan) Bake for approximately 15 minutes, or until golden. Allow scones to cool and prepare glaze.
In a small bowl, combine all of the glaze ingredients and whisk until smooth. Drizzle glaze over cooled scones and allow glaze to harden.