In a large mixing bowl or stand mixer fitted with the paddle attachment, cream together the vegan butter and granulated sugar for about 3 minutes, until light, fluffy, and pale in color. This step helps create the soft texture.
In a separate bowl, sift together the flour, cornstarch, cream of tartar, baking powder, and baking soda. Set aside.
Add the vegan yogurt, vanilla extract, and almond extract to the butter and sugar mixture. Mix until smooth and fully combined.
Using a spatula, gently fold the dry ingredients into the wet ingredients just until no dry flour remains. The dough will be softer and slightly sticky , do not overmix.
Cover the bowl tightly with plastic wrap and refrigerate the dough for 1 hour. This step is essential to prevent spreading and achieve the classic Lofthouse shape.
Prepare your vegan buttercream while you wait for your cookies to chill. Add a drop of red food coloring to create a light pink color.
Once cookies are chilled, preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
Scoop and roll the dough into evenly sized balls, spacing them a few inches apart on the baking sheet. Place the cookies in the freezer for 7 minutes before baking.
Bake for 12 minutes, until the edges are set and the tops look slightly matte. The centers may appear soft but will continue to set as they cool.
Allow cookies to cool on the baking sheet for 10 minutes, then transfer to a wire rack to cool completely.
Once fully cooled, frost each cookie with vegan buttercream, smoothing the frosting with the smooth side of a knife or offset spatula. Finish with sprinkles if desired.