In the bowl of a stand mixer (or a medium bowl), whip the butter with the paddle attachment (or electric hand mixer) for about 1-2 minutes until it is light and fluffy. It will change color and become a little lighter.
Add the powdered sugar and vanilla extract, mix well with the hand blender. Scrape down the sides if needed.
Add the 2 teaspoons lemon zest, 1-1/2 tablespoons lemon juice, flour, and salt. Mix only until it combines into a soft dough.
Cover the bowl with plastic wrap and refrigerate for 30 minutes.
While you are waiting for the dough to chill, pre-heat your oven to 350 F and prep your cookie sheet with the silicone mat or parchment paper.
Portion out the dough with the small cookie scoop (about 2 tablespoons) onto the sheet pan. They don't spread too much, but leave a little bit of room (2 inches) in between just incase.
Bake on the middle rack for 12-15 minutes, check for browning at around 10 minutes. They should only be very lightly browned around the bottom edges.
Cool on the pan for 10 minutes, then transfer to the cooling racks for another 30 minutes before icing.
While the cookies are cooling, mix together the powdered sugar, lemon zest, and enough juice to make an icing. It should be pourable but not like water, it will drizzle nicely and stick to the cookie when dipped. Make adjustments as needed. Cover and set aside until ready.
Dip the tops of the cookies in the icing and let the excess drip off. Sometimes I have to tip the bowl to allow enough "room" for dipping. Place back onto the cooling rack until full set and dry, that time can vary but you want it set before serving.
When set, transfer to a plate for serving or store them in an air-tight container at room temperature for 3 days or up to 1 week in the fridge.
Notes
Nutritional values and servings are estimates only.