Preheat oven to 350℉. Prepare a large baking sheet with a non-stick spray, or parchment paper, set aside.
In large mixing bowl beat the butter for a few seconds, then pour in the sugar and cream together until fluffy.
Add in the lemon zest, vanilla, lemon juice and egg. Continue to mix until smooth.
To the same bowl add the flour, baking soda, and salt.
Mix until fully combined.
Drop cookie dough by the spoonful onto the prepared cookie sheet. Bake until just starting to turn a light golden color on the edges, approximately 10 minutes. Remove from oven, let cool on the cookie sheet about 2-3 minutes and then remove to continue cooling on a wire rack.
Once cooled prepare the glaze by whisking the powdered sugar, lemon juice, and lemon zest together until well combined. Spoon onto the top of the cookies or drizzle. Allow to sit and dry, glaze will harden.
Store cookies in airtight container at room temperature.