Place the almonds in a high-powered blender or food processor and pulse until slightly irregular pieces, double the size of rice grains, form. (Alternatively, chop finely with a knife.) Transfer to a large bowl, then, using a fine-mesh sieve, sift in the flour, cinnamon, baking soda, baking powder, and salt.
In a medium bowl, combine the cane sugar and coconut oil and beat with a fork until blended thoroughly. Add the plant-based milk and beat until the ingredients are uniformly combined. Transfer to the large bowl and use a spoon to mix into the dry ingredients until evenly combined and doughy enough to knead with clean hands.
Form the dough into one large ball, then place in a bowl or container, cover, and refrigerate at least 6 hours (or up to overnight, for best results).
Preheat the oven to 350°F. Line two baking sheets with parchment paper or silicone baking mats.
Remove the dough ball from the refrigerator and let it come to room temperature, about 30 minutes. Dust a work surface with flour and then roll out the dough to about 1⁄2-inch thick. Using a 4-inch cookie cutter or a cup, stamp out rounds from the dough and transfer to the prepared baking sheets. Reroll the scraps of dough to stamp out more rounds.
Bake the cookies until lightly browned around the edges, about 12 minutes.
Remove cookies from the baking sheets and transfer to a wire rack. Let cool completely, then dust with confectioners’ sugar.
Store the cookies in an airtight container at room temperature for up to 8 days.