Line two baking sheets with parchment paper and set aside. In a medium bowl, whisk together the flour, cornstarch, and salt. I like to sift these together to ensure the cornstarch distributes evenly—it helps create a more tender cookie texture. Set this dry mixture aside while you prepare the butter mixture.

In a large bowl, beat the room-temperature butter and sugar together for about 5 minutes until the mixture is light, fluffy, and pale in color. This creaming process incorporates air into the dough, which helps the cookies rise slightly and creates a tender crumb. Stop occasionally to scrape down the sides of the bowl to ensure even mixing.

Add the vanilla extract to the creamed butter and sugar, then mix until combined. Gradually add the dry ingredient mixture from Step 1 in two parts, mixing on low speed after each addition until just combined. Avoid overmixing once the flour is added, as this can develop gluten and make the cookies tough. The dough should come together without any visible streaks of flour.

Using a small cookie scoop or your hands, form the dough into 1-inch balls and place them about 2 inches apart on the prepared baking sheets. Gently press your thumb into the center of each ball to create a thumbprint indentation—don't press all the way through to the bottom. Cover the baking sheets with plastic wrap and refrigerate for at least 2 hours (or up to overnight). This chilling is essential because it prevents the cookies from spreading too much during baking and helps them hold their shape.

Preheat your oven to 350°F (175°C). Remove the chilled dough from the refrigerator and carefully spoon about 1/4 to 1/3 teaspoon of strawberry jam into each thumbprint. I find it helps to use a very small spoon so you don't overfill—too much jam can leak out during baking. Bake for 14-16 minutes, until the edges are light golden brown but the centers still look slightly underdone. They'll continue to cook as they cool.

Allow the cookies to rest on the baking sheets for 5 minutes to set, then transfer them to a wire cooling rack to cool completely. While the cookies cool, prepare the glaze by whisking together the sifted powdered sugar and milk in a small bowl until smooth and pourable. Add more milk one drop at a time if the glaze is too thick, or a bit more powdered sugar if it's too thin.

Once the cookies are completely cool, drizzle the glaze over each one using a fork or small spoon. Work over parchment paper to catch any drips. Allow the glaze to set for a few minutes before serving. These cookies stay fresh in an airtight container for up to 5 days.