3/4 cup unsalted butter, at room temperature
3/4 cup granulated sugar
1 heaping, tightly packed Tbs. finely grated lemon zest
1 tsp. pure vanilla extract
1 large egg
1 large egg yolk
2 cups all-purpose flour
1/2 tsp. kosher salt
24 lollipop sticks
For the glaze:
1 cup confectioners’ sugar
2 Tbs. lemon juice
Sprinkles, food coloring, or other decorations (see note; optional)
In the bowl of a mixer fitted with the paddle attachment, beat the butter and granulated sugar on medium-high speed until creamy. Add the zest, vanilla, egg and egg yolk and beat until smooth. Add the flour and salt and beat on low speed until the crumbly dough comes together. Cover the bowl and refrigerate the dough until chilled and firm, about 2 hours.
Space 2 racks evenly in the oven and preheat to 350 degrees F. Line 2 baking sheet with parchment paper.
On a lightly floured work surface, roll out the dough 1/4 inch thick. using a 3-inch flower-shaped or fluted cutter, cut out cookies. Insert a stick into each one, pushing it about midway through. Use a spatula to put the cookies on the prepared pans, spacing them slightly apart (you might need to bake the cookies in batches).
Bake until the cookies are very lightly golden, 10 to 12 minutes, rotating the pans about halfway through. Let the cookies cool on the pans for at least 15 minutes, then transfer to wire racks to cool completely.
To make the glaze, in a bowl, stir together the confectioners’ sugar and lemon juice until smooth. You can separate it into different bowls and add food coloring if you want to get fancy. Smear the glaze on the cookies and decorate with sprinkles or designs (see Note), if desired. Makes about 2 dozen cookies.