In a large mixing bowl, combine the softened coconut oil and packed dark brown sugar. Mix with a spoon or spatula until smooth and well combined.
Add the vanilla extract and stir until incorporated.
Add the flour, baking powder, and salt. Stir until mostly combined.
Add 1 to 2 tablespoons of cold water, just enough to bring the dough together. Mix until the dough holds its shape but isn't sticky.
Turn the dough out onto a clean surface and form it into a square log, about 1½ inches wide and tall. (A square shape is easier to slice evenly than a round log.)
Wrap the dough tightly in plastic wrap and chill in the refrigerator for at least 1 hour, or until firm.
Preheat the oven to 325°F (160°C). Line a large baking sheet with parchment paper or a silicone baking mat.
Once chilled, slice the dough into ¼-inch thick cookies. Arrange them on the prepared baking sheet, spacing them about ½ inch apart.
Bake for 18 to 20 minutes, or until the edges are golden and the cookies are just firm to the touch.
Let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.