Preheat your oven to 325°F (165°C). Line a baking sheet with parchment paper for slice-and-bake cookies, or lightly butter (or line with parchment) an 8- or 9-inch round or square baking pan if making pan-style wedges or bars.

In a large mixing bowl, beat the softened unsalted butter and powdered sugar together for 2–3 minutes, until the mixture looks pale, smooth, and creamy. Use a hand mixer on medium speed or a sturdy wooden spoon if mixing by hand.

Beat in the vanilla extract and fine sea salt until fully combined, so the flavor and seasoning are evenly distributed throughout the dough.

In a separate bowl, whisk together the all-purpose flour and cornstarch (if using). Gradually add this dry mixture to the butter mixture, mixing on low speed or stirring by hand just until the dough comes together into soft, slightly crumbly clumps that hold when pressed in your hand. If the dough is very dry and won’t clump, sprinkle in 1–2 teaspoons of milk or cream, a little at a time, just until it holds together.

For slice-and-bake cookies: Turn the dough out onto a lightly floured surface. Gently press and roll it into a log about 2 inches (5 cm) in diameter. Wrap the log tightly in plastic wrap and chill for 30–45 minutes, or up to 3 days, until firm. When ready to bake, slice the chilled dough into 1/4–1/3-inch thick rounds and place them on the prepared baking sheet, spacing them slightly apart.

For pan-style wedges or bars: Press the dough evenly into the prepared round or square pan. Use the bottom of a measuring cup or glass to smooth the surface. With a sharp knife, lightly score the dough into wedges (for a round pan) or bars (for a square pan) so it will be easier to cut clean pieces after baking.

Use a fork to gently prick (dock) the tops of the cookies or the surface of the pan of dough to help steam escape and keep the shortbread flat and even. If desired, sprinkle the tops lightly with coarse sugar for sparkle and extra crunch.

Bake at 325°F (165°C) until pale and set with just a hint of light golden color at the edges. For slice-and-bake cookies, bake 14–18 minutes. For pan shortbread, bake 25–35 minutes. Do not let the cookies turn deep brown; they should remain mostly pale for a tender, classic shortbread texture.

For pan-style shortbread, remove from the oven and immediately re-cut along the score lines while still warm. Let cool completely in the pan so the cookies can firm up, then lift out (if using parchment) and separate the pieces. For sliced cookies, let them cool on the baking sheet for 5–10 minutes, then transfer to a wire rack to cool completely before serving.