3 sticks unsalted butter, at room temperature

3 cups firmly packed light brown sugar

3 eggs

1 tbsp vanilla extract

3 1/2 cups all-purpose flour

1 cup plus 2 tbsp unsweetened cocoa powder

1 ½ tsp. baking soda

1 ½ tsp. cream of tartar

¾ tsp. salt

¼ cup coarse sugar, or as needed

In a large bowl, using an electric mixer, beat the butter and brown sugar on medium speed until creamy. Add the eggs and vanilla and beat until smooth. In another bowl, stir together the flour, cocoa powder, baking soda, cream of tartar and salt. Reduce the speed to low, add the flour mixture to the butter mixture and beat until blended.
Divide the dough into 3 equal pieces, pat each into a flat disk and wrap separately in plastic wrap. Refrigerate 1 disk for at least 1 hour to use now, and store the remaining 2 disks for future use (see note above).
Preheat an oven to 350°F (180°C). Line 2 baking sheets with parchment paper.
On a work surface, place the disk between 2 sheets of plastic wrap and roll out about 1/8 inch (3 mm) thick. Use a cookie cutter to shape the dough. Sprinkle the cookies with the coarse sugar.
Bake the cookies until the edges are crisp, 8 to 10 minutes. Let the cookies cool.

2 sticks unsalted butter, softened

1 cup confectioners’ sugar

1 tbsp finely grated lemon zest

1 ½ tbsp fresh lemon juice

2 cups all-purpose flour

¾ tsp salt

For the Glaze:

½ cup plus 2 tbsp confectioners sugar

1 tbsp fresh lemon juice

1 tbsp unsalted butter, softened

Finely grated lemon zest, for garnish

Preheat the oven to 350° and position racks in the upper and lower thirds. In a large bowl, using a handheld electric mixer, beat the butter with the confectioners' sugar until very smooth, about 2 minutes. Beat in the lemon zest and juice, then beat in the flour and salt until just incorporated; scrape down the fresh lemon juice side of the bowl as necessary.
Roll half of the dough into 1-inch balls. Arrange the balls 1 inch apart on 2 baking sheets and, gently flatten each cookie. Bake for 12 to 14 minutes, until the cookies are lightly browned on the bottom and just firm; shift the baking sheets from top to bottom and front to back halfway through baking. Let the cookies cool on the baking sheets for 2 minutes, then transfer them to a rack to cool completely.

For the Glaze:

In a bowl, whisk the confectioners' sugar with the lemon juice and butter until smooth.
Spread the lemon glaze on the cooled cookies and garnish with finely grated lemon zest. Let the cookies stand until glaze is set, about 15 minutes.