Set the oven to 350 degrees Fahrenheit. Paper liners should be used to line a 12-cup muffin pan. Nonstick cooking spray should be used to coat the liners.
To make the cake, combine the flour, granulated sugar, baking soda, baking powder, and salt in a medium basin and whisk to combine. In a different medium bowl, combine the almond milk, brown sugar, oil, and vanilla. It's okay if there are lumps when you add the almond milk mixture to the flour mixture and gently fold to incorporate. Evenly distribute the batter among the lined pans.
Bake the cupcakes for 20 to 22 minutes, or until a toothpick inserted in the center of one comes out clean and the tops are golden brown. After a few minutes of cooling in the pan, remove to a rack to finish cooling.
For the frosting, beat the margarine for about a minute on medium-high in the paddle attachment-equipped bowl of a stand mixer (or in a big basin if using a hand mixer). Beat the frosting on low for about a minute, until it comes together and is smooth, after which you may add the confectioners' sugar, almond milk, and vanilla.