Whisk the dry ingredients. In a medium bowl, whisk together the flour, cornstarch, baking powder, and salt. Set aside.

Cream butter and sugar. In a large bowl, beat the butter and granulated sugar on medium speed until light and slightly fluffy, about 2–3 minutes. Don’t overbeat; you want air, not whipped butter.

Add eggs and flavoring. Beat in the egg and egg yolk until fully combined. Mix in the vanilla and almond extract.

Combine wet and dry. Add the dry ingredients in two additions, mixing on low just until the dough comes together. It should be soft and not sticky.

Chill the dough. Divide dough in half, flatten each into a disk, wrap tightly, and refrigerate for at least 1 hour (or up to 2 days). Chilled dough prevents spreading and makes rolling easier.

Preheat and prep. Heat oven to 350°F (175°C). Line baking sheets with parchment paper.

Roll and cut. On a lightly floured surface, roll one dough disk to about 1/4 inch thick. Dip the tree cutter in flour, then cut cookies close together. Transfer to the lined sheets, spacing about 1 inch apart. Gather scraps, chill briefly if warm, and reroll.

Bake. Bake 9–11 minutes, until the edges look set and just barely golden on the bottom. The tops should stay pale. Cool on the baking sheet 5 minutes, then move to a rack to cool completely.

Make the icing. In a bowl, whisk powdered sugar, 2 tablespoons milk, corn syrup, and vanilla until smooth. Add a tiny amount of green gel coloring until you reach a tree-green shade. Adjust consistency: add milk by the teaspoon for a flow that ribbons off the whisk and smooths in 10–15 seconds; add powdered sugar to thicken for outlining.

Decorate. For neat edges, use a thicker icing to outline the tree, then thin icing to flood the center. Gently nudge icing into corners with a toothpick. Add sprinkles while the icing is wet. Let set at room temp until dry to the touch, 2–4 hours, or overnight for full set.