Line two baking sheets with parchment paper or silicone baking mats; set aside.

In the bowl of a stand mixer fitted with the paddle attachment, combine 1 cup (8 oz) unsalted butter (softened), 1 cup (200 g) superfine sugar, and 1/2 teaspoon salt. Beat on medium speed, scraping down the sides and bottom of the bowl as needed, until the mixture is light and fluffy and noticeably lighter in color, about 3 minutes.

Add 1 large egg and beat until incorporated. Add 1 egg yolk and 2 teaspoons vanilla extract and beat until fully combined.

With the mixer on low speed, add 2 1/2 cups (350 g) all-purpose flour and mix just until the dough comes together. Stop as soon as there are no visible streaks of flour—do not overmix.

Divide the dough into two equal portions. Wrap each portion tightly in plastic wrap. Refrigerate the wrapped dough for at least 1 hour and up to 48 hours, until firm and not sticky. (If your kitchen is warm or the butter was very soft, chilling may take longer than 1 hour.)

When ready to roll, place a wrapped portion on a lightly floured work surface. Dust the rolling pin and surface with flour as needed. Roll the dough to 3/8-inch thickness.

Use a 3-inch heart cookie cutter to cut shapes from the dough. Transfer cut cookies to the prepared baking sheets using a thin spatula to keep them intact. Re-roll scraps as needed, keeping the dough chilled between rolls if it becomes too soft.

Refrigerate the cut cookies on the baking sheets for 15 minutes to re-firm them (this helps prevent spreading). While the cookies chill, preheat the oven to 375°F (190°C).

Bake the chilled cookies on the prepared sheets until the bottoms and edges are just beginning to turn golden, about 9–12 minutes (longer if you used larger cutters). Rotate sheets once halfway through baking if your oven cooks unevenly.

Transfer cookies to a wire rack and allow to cool completely before icing.

To make the cinnamon icing, place 2 cups (240 g) powdered sugar and 1 teaspoon cinnamon in a medium bowl. Stir in 2 tablespoons milk (add the milk gradually—start with about half and add the rest as needed, but do not exceed the 2 tablespoons) and 1/2 teaspoon vanilla extract until the mixture is smooth and spreadable.

Stir in 2 teaspoons light corn syrup and 20–30 drops red food coloring until the icing is glossy and evenly colored. The icing should be thin enough that a line drawn through it with a knife fills back in within 8–10 seconds.

Dip each cooled cookie into the icing or spread the icing onto the cookie; scrape off excess with the side of the bowl or a knife. Pop any air bubbles with a toothpick.

Let the iced cookies dry on a wire rack until the icing is set. They will be dry enough to eat in under an hour but allow at least 4 hours before stacking or packing.