In a large bowl, stir together the oat flour, baking powder, and sugar. Stir in the remaining ingredients (non-dairy milk, oil, and vanilla extract) until just incorporated.
Heat a non-stick pan to medium-low heat. If you don't have a really good non-stick pan, melt a little vegan butter or oil in the pan. Scoop about ¼ cup of batter into the pan for each pancake.
Cook until the top of the pancake starts to bubble and the bottom is golden brown (about 3-4 minutes). Flip! Cook until that side is golden brown (about 1-2 minutes)