In a medium bowl, whisk together the all-purpose flour, cornstarch, baking powder, baking soda, and fine sea salt until well combined. Set aside.

In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the granulated sugar and softened vegan butter on medium speed for 2–3 minutes, until the mixture looks light and slightly fluffy. Scrape down the sides of the bowl as needed.

Add the neutral oil, vanilla extract, and almond extract (if using). Mix on low speed at first so it doesn’t splatter, then increase to medium and beat until the mixture is smooth and glossy.

Pour in the non-dairy milk and mix again just until combined. The mixture may look slightly curdled or split at this stage; this is normal and will smooth out once the dry ingredients are added.

Add the dry ingredient mixture to the bowl in two batches, mixing on low speed just until no visible streaks of flour remain. Scrape down the sides and bottom of the bowl to ensure everything is incorporated. The dough should be soft but not sticky, similar to play dough. If it feels very sticky, you can sprinkle in 1–2 extra tablespoons of flour, but avoid adding too much.

Divide the dough into two equal portions and flatten each into a disk. Wrap each disk tightly in plastic wrap or parchment paper and chill in the refrigerator for at least 1–2 hours, or up to 3 days. Chilling allows the flour to hydrate, firms up the fat, and helps the cookies hold their shape.

When ready to bake, preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats. If the dough is very firm, let it sit at room temperature for 5–10 minutes to soften slightly.

Lightly flour your work surface and rolling pin. Working with one disk at a time, roll the dough out to about 1/4 inch (6 mm) thickness for softer cookies, or slightly thinner if you prefer crisper edges. If the dough cracks at the edges, gently press it back together with your fingers.

Use cookie cutters to cut out shapes from the rolled dough. Transfer the cut cookies to the prepared baking sheets, spacing them about 1–2 inches apart. Gather the scraps, gently press them together, and re-roll once or twice to cut more cookies.

If you are serving the cookies plain or only lightly decorated, sprinkle the tops with a little extra granulated sugar before baking. You can also add vegan colored sugar for a simple decoration at this stage.

Bake one sheet at a time in the preheated oven for 8–11 minutes, depending on the size and thickness of your cookies. The edges should look set and just barely golden, while the centers remain pale. They will continue to firm up as they cool, so avoid overbaking.

Allow the cookies to cool on the baking sheet for about 5 minutes, then transfer them carefully to a wire rack to cool completely. Make sure they are fully cooled before adding any frosting or icing.

Once the cookies are completely cool, decorate with vegan frosting or icing and vegan sprinkles or colored sugar as desired. Let any icing set before stacking or storing.