In a medium-sized mixing bowl mix butter and white sugar. Add the egg and continue to mix until combined.
Stir in the lemon zest. Add flour in batches until totally mixed.
Take about 2 tsp. of the dough and shape it into a ball in your hands. Place onto a parchment paper-lined cookie sheet and flatten just a little.
Bake for 8 minutes.
Remove and after a few minutes transfer to a wire cooling rack. Cookies will need to be completely cooled before glazing.
In a small mixing bowl add the confectioner’s sugar, lemon juice, and cream and stir until combined.
Spoon a little onto each cookie spreading toward the edges. Decorate with a little lemon zest. The glaze will take about 15 minutes to set, before eating.