Make the sugar cookie dough: Whisk flour, baking powder, and salt. In a separate bowl, beat butter and sugar until creamy, 2–3 minutes.
Beat in egg and vanilla. Add dry ingredients and mix just until combined.
Chill for clean shapes: Divide dough in half, flatten into discs, wrap, and chill for at least 1 hour. Chilled dough prevents spreading and gives clean edges.
Roll and cut: Flour your surface.
Roll to 1/4 inch thickness. Cut heart shapes and place on parchment-lined sheets. Chill 15 minutes while the oven preheats to 350°F (175°C).
Bake sugar cookies: Bake 8–10 minutes, until set and just barely golden on the edges.
Cool completely before glazing.
Make the chocolate shortbread: Beat butter and powdered sugar until smooth. Sift in flour, cocoa, and salt. Add vanilla and mix until a soft dough forms.
If crumbly, knead lightly to bring together.
Form into a log and chill: Shape dough into a 2-inch diameter log, wrap tightly, and chill at least 1 hour (or freeze 20–30 minutes) for neat slices.
Slice and bake: Preheat oven to 325°F (165°C). Slice 1/4-inch rounds and place on lined sheets. Bake 12–15 minutes, until edges are firm.
Cool on the sheet 5 minutes, then transfer to a rack.
Mix the pink glaze: Whisk powdered sugar, 2 tablespoons milk, vanilla, and salt until smooth. Add more milk 1 teaspoon at a time to reach a thick-but-pourable consistency. Tint with a drop or two of food coloring.
Decorate: Dip the tops of sugar cookies or drizzle the shortbread with glaze.
Add sprinkles immediately before the glaze sets. Let cookies dry at room temperature until the glaze is firm, 1–2 hours.
Package for gifting: Layer cookies with parchment in tins or boxes. Add a note card and tie with ribbon.
Keep them cool and dry until gifting.