• ¾ cup (6 oz/185 g) unsalted butter, at room temperature
• 1 cup (8 oz/250 g) sugar
• 4 large eggs
• 2 teaspoons vanilla extract
• Kosher salt
• 3½ cups (17½ oz/540 g) (all-purpose) flour
• ½ cup (3 oz/90 g) colored sprinkles

In a stand mixer fitted with the whisk attachment, beat together the butter and sugar on high speed until creamy, about 2 minutes. Add 3 of the eggs, one at a time, beating on high speed after each addition until combined. Add the vanilla and beat until combined, about 2 minutes longer. Switch to the paddle attachment and add 1 teaspoon salt and then add the flour, ½ cup (2½ oz/75 g) at a time, beating on medium speed until the dough is soft and holds together without being sticky. Add the flour gradually to achieve a smooth dough (you may not need all of it). Stir in the sprinkles.

Divide the dough into 2 equal balls and wrap separately in plastic wrap. Place in the fridge for at least 1 hour or up to 3 days. The dough will keep in the freezer for up to 1 month. If using frozen dough, let it thaw in the fridge overnight or for about 1 hour at room temperature. The dough should be cold when you cut out the cookies.

Preheat the oven to 350°F (180°C).

Place a piece of parchment paper that is the same size as a baking sheet on your counter and place a ball of the dough on the parchment. Place a second piece of parchment over the dough. Roll out the dough ¼ inch (6 mm) thick. Peel off the top parchment and use 1 or more cookie cutters to cut out shapes, spacing them 1 inch (2.5 cm) apart. Alternatively, use an overturned glass to cut out rounds. Keep the cookies on the parchment and pull away the excess dough. Shape the excess dough into a ball, place between parchment sheets, roll out ¼ inch (6 mm) thick, and cut out more cookies.

Transfer the parchment paper with the cookies to a baking sheet. In a small bowl, beat the remaining 1 egg, then brush the cookies with it.

Bake the cookies until golden, 10–15 minutes. Let cool on the baking sheet for 15 minutes, then transfer to a wire rack to cool completely. While the first pan of cookies is baking, repeat with the second ball of dough to make more cookies. Bake a third batch of cookies from any excess dough scraps. The cookies will keep in an airtight container at room temperature for up to 2 weeks.