Add the softened butter and granulated sugar to a medium mixing bowl or the bowl of a stand mixer. Beat with a hand mixer or stand mixer on medium speed for 2–3 minutes, until the mixture looks pale, creamy, and a bit fluffy. If mixing by hand, beat vigorously with a wooden spoon until lighter in color.

Mix in the vanilla extract and fine sea salt, if using. Stir just until evenly combined.

Sprinkle the all-purpose flour over the butter mixture in 2 batches. Mix on low speed after each addition just until the flour is incorporated and a soft dough begins to form. It may look crumbly at first—keep mixing gently and it will come together. If it is very crumbly and will not press together, gently knead it a few times with clean hands.

Turn the dough out onto a clean counter or a sheet of parchment paper. Use your hands to press it into a cohesive ball, then flatten into a disk. The texture should feel soft but not sticky. If it sticks a lot to your hands, knead in 1–2 tablespoons more flour as needed.

Wrap the dough disk tightly in plastic wrap or place it in a covered container. Chill in the refrigerator for 30–60 minutes to help the cookies keep their shape and develop slightly crisper edges. You can skip chilling for a faster cookie, but expect more spreading.

While the dough chills, preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat.

Scoop about 1 tablespoon of dough for each cookie and roll into balls with your hands. Place the dough balls on the prepared baking sheet, spacing them about 2 inches apart. For a traditional sugar cookie look, gently press each ball down with the bottom of a glass or your fingers to about 1/4–1/3 inch thick. If desired, sprinkle a little granulated or coarse sugar on top, or roll in colored sanding sugar.

Bake at 350°F (175°C) for 10–12 minutes, or until the edges are just set and the bottoms are a light golden color. The tops will remain pale. Begin checking around 9 minutes, especially if your oven runs hot.

Let the cookies cool on the baking sheet for 5 minutes; they will be very soft when they first come out of the oven. Then transfer them to a wire rack to cool completely. They will firm up as they cool, with a tender, melt-in-your-mouth texture.