Preheat oven to 350 degrees F and line a large baking tray with parchment paper.
Mix the flour, cornstarch, baking powder, and salt together in a bowl and set aside.
Beat the softened vegan butter and sugar together in a stand mixer or using an electric handheld mixer for 2 minutes or until it comes together. Scrape the sides of the bowl and beat again for another minute, until light and fluffy. Add in the almond milk and extracts and mix until combined.
Slowly combine the dry with the wet and beat until a dough has formed - about 2-3 minutes of mixing. Do not overmix - once the dough comes together, it’s ready.
Move the dough to a floured surface. Roll the dough out to ¼ inch in thickness. Use a cookie cutter to cut out your cookies and carefully transfer them to a parchment lined cookie sheet, 1 inch between each cookie. Continue to re-roll the dough and cut out cookies until you have used all the dough.
Place the sheet in the fridge for 10 minutes. This step is crucial for the cookies to maintain their shape or design. Bake straight from the fridge for 10-12 minutes, until slightly golden around the edges. Remove and allow to cool.
Whisk together the ingredients for the icing and dip the cooled sugar cookies in the icing. Top with vegan sprinkles if desired!