Combine the milk, eggs, and vanilla in a blender and puree to combine.
Sift the flour, sugar, baking powder, and salt together and add to the blender. Pulse to combine.
Let the batter rest for at least 30 minutes before cooking (you can also make it the night before and stash it in a covered jar in the fridge).
When you're ready to cook, heat a small non-stick skillet over a medium-high flame. Pour 2-3 tablespoons of the batter into the pan and tilt it so that it spreads to over the bottom of the pan.
Let the crepe cook until the batter is set and doesn't look at all drippy and the edges begin to pull away from the sides of the pan. This will take 2-3 minutes in the beginning, and just 60 to 90 seconds as the pan heats up.
Carefully run a thin spatula around the edges of the crepe to loosen it from the pan and flip it. Let it cook for 15-30 seconds on this side.
Slide the crepe out of the pan and onto a plate. Repeat with remaining batter.
You should get 12-15 pancakes from this recipe.