In a medium bowl, use a wooden spoon to combine the flour, baking powder, baking soda, and salt. Set aside.
Place the room-temperature non-dairy butter and granulated sugar in a large bowl. Use a hand mixer to cream the butter and sugar together until smooth and well-combined.
Add the non-dairy milk, non-dairy sour cream, vanilla extract, and almond extract to the wet ingredients and beat with the hand mixer until completely incorporated. Add the flour mixture to the wet ingredients and beat to combine, 1-2 minutes.
Place a piece of parchment paper on a flat surface. Gather one half of the cookie dough into a loose ball and place it on top of the parchment paper, then cover with another piece of parchment paper, and gently flatten.
Use a rolling pin to roll out the dough (on top of the parchment paper) to about ¼" thick. Transfer the parchment paper and dough to a half-sheet pan. Repeat this process with the other half of the cookie dough, and place both pans in the fridge for 45 minutes to 1 hour.
Preheat the oven to 350℉. Place the parchment paper and dough on a flat surface and remove the top sheet of paper. Use your preferred cookie cutters to shape the cookies, and place them on the pans. Repeat with the second half of the dough.
Bake for 12-14 minutes, until the cookies are just barely golden brown around the edges. Allow them to cool on the sheet pan for 15 minutes, then transfer to a cooling rack to cool completely.
Make the icing. Combine the powdered sugar with the non-dairy milk and light corn syrup in a medium bowl and whisk well until completely smooth. If desired, add food coloring and whisk until the color is consistent throughout. Using an icing spatula or small offset spatula, carefully spread the icing onto each cookie. If desired, add sprinkles, decorating sugar, or other toppings. Allow the icing to fully set before enjoying.