Preheat the oven to 350F. Line a mini muffin tin with parchment paper baking cups.
In a stand mixer fitted with the paddle attachment, beat together the coconut sugar, coconut oil, and vanilla on high speed for 1 minute.
In a medium mixing bowl, whisk together the oat flour, baking powder, and sea salt. Place within reach of the mixer.
With the mixer off, add the water to the coconut sugar mixture and start beating while slowly adding the oat flour mixture. Beat for 30 seconds, or until the dough pulls together into large, moist mounds as it moves around the mixing bowl. When you first add the dry ingredients, the dough will be dry and crumbly; however, just keep beating on high—the finished dough will look and feel similar to Play-Doh. If the dough is still dry and crumbly after beating for 30 seconds, add more filtered water, 1 tablespoon at a time, and continue beating until it pulls together.
Scoop approximately 1 1/2 tablespoons of the dough into each baking cup, dividing any extra dough evenly among the 12 baking cups. Use your fingers to press the dough firmly and evenly into the bottom and 1 inch up the sides of each cup, forming a well.
Bake for 10 to 14 minutes, or until the crusts are golden brown and a toothpick inserted into the center of one comes out mostly clean with a few moist crumbs at the tip. If you prefer a soft, chewy, cookielike crust, bake for 10–12 minutes; if you prefer a crisper crust, bake for 12–14 minutes. They'll puff up quite a bit while baking; however, they'll fall and settle back into crust shape as they cool. Also, don't worry if there is an oily sheen to the crusts when you first remove them from the oven; the oil will be reabsorbed as they cool.
Transfer the pan to an oven-safe cooling rack. Cool completely.