Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, cream the dairy-free butter and granulated sugar together using an electric mixer or stand mixer until light and fluffy.
Add the unsweetened almond milk and pure vanilla extract to the butter-sugar mixture, and continue to mix until well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until the dough comes together. Be careful not to overmix.
Form the cookie dough into a ball and wrap it in plastic wrap. Chill the dough in the refrigerator for at least 30 minutes to firm up.
On a lightly floured surface, roll out the chilled cookie dough to about 1/4-inch (6mm) thickness. Use cookie cutters to cut out desired shapes.
Place the cut-out cookies on the prepared baking sheet, leaving a little space between each cookie.
Bake the cookies for 8-10 minutes or until the edges are lightly golden brown. Be careful not to overbake; the cookies will continue to firm up as they cool.
Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.