Line 2 baking sheets with parchment paper or silicone baking mats. Preheat the oven to 350°F (175°C).
In a large mixing bowl, beat the softened butter and granulated sugar with a hand mixer or stand mixer on medium speed for 2–3 minutes, until the mixture is pale and fluffy.
1 cup unsalted butter, 2/3 cup granulated sugar
Beat in the egg and vanilla extract until fully combined, scraping down the sides of the bowl as needed. The mixture should be smooth and creamy.
1 large egg, 2 teaspoons pure vanilla extract
In a separate bowl, whisk together the all-purpose flour and fine sea salt.
2 cups all-purpose flour, 1/4 teaspoon fine sea salt
Add the flour mixture to the butter mixture in two additions, mixing on low speed just until no dry spots remain. The dough will be thick; avoid overmixing.
2 cups all-purpose flour, 1/4 teaspoon fine sea salt
If piping the dough into swirls, add milk or heavy cream 1 teaspoon at a time, beating on low until the dough is just soft enough to pipe but still thick and able to hold its shape. If scooping or rolling, you may not need any liquid.
2 teaspoons milk or heavy cream
For piped swirls: Transfer dough to a piping bag fitted with a large open star tip and pipe 1.5–2 inch circles or rosettes onto the prepared sheets, spacing about 2 inches apart. For scooped cookies: Use a small cookie scoop or tablespoon to portion dough into balls, place on sheets, and flatten slightly. For log-and-slice cookies: Roll dough into a 2-inch-diameter log, wrap in plastic, chill 30–45 minutes, then slice into 1/4-inch rounds.
If desired, sprinkle the tops with coarse sugar or sprinkles, or gently press chopped nuts onto each cookie.
3 tablespoons coarse sugar or sanding sugar, colored sprinkles or nonpareils, finely chopped nuts
Bake one sheet at a time for 9–12 minutes, or until the edges are lightly golden and the centers look set but not browned. For extra-crispy cookies, bake 1–2 minutes longer, watching closely.
Let the cookies cool on the baking sheet for 5 minutes to firm up, then transfer to a wire rack to cool completely.
Once the cookies are completely cool, dip half of each cookie into melted chocolate, then place on parchment until the chocolate is set.
1/2 cup melted dark or milk chocolate