Preheat oven to 350°F.
Using a mortar & pestle or a spice grinder, combine the sugar and lemon zest together. I opted to just blend them together with my fingers until the zest was distributed and the sugar was fragrant.
In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, baking soda, salt, and cold butter, and beat on low speed until the mixture is crumbly and resembles coarse cornmeal. Add the sugar/zest mixture, cream, and vanilla, and continue to mix until it clumps together and a dough is formed.
If the dough is too soft, it can be wrapped in plastic and refrigerated for about 30 minutes before continuing. Otherwise, on a lightly floured surface, a silpat sheet, or a sheet of wax or parchment paper (whatever your preference), roll the dough out to ¼? thickness (or ½" if you want to try the original recipe recommendation – maybe it'll work better for you). Using a ruler as a guide, square off the edges and cut the dough into 1" squares with a sharp knife or a pizza cutter.
Transfer the squares to your baking sheet, about 2" apart, and sprinkle lightly with sanding sugar. Bake for about 10-12 minutes, until lightly golden brown, rotating the baking sheet halfway through. Allow to cool on a wire rack for a few minutes before removing the cookies from the pan and allowing them to cool completely.
