Add the rolled oats, milk, and vanilla extract to a blender. Blend on high until completely smooth.
Add the eggs and pulse until just combined.
Heat a frying pan on medium heat and add butter or oil. Once melted, pour about 2–3 tablespoons of the crepe mixture into the pan. Swirl the pan to spread the batter thinly.
Cook until small bubbles form and the edges look set, then flip and cook the other side until golden.
Repeat with the remaining mixture (makes about 6 crepes).
Serve warm with toppings of choice such as chia jam, ricotta, or cream cheese.