Mix flour, 1 cup milk, and eggs together in a large bowl. Stir butter, sugar, and vanilla extract into flour mixture until smooth. Add remaining 1 cup milk; mix until just blended.

Heat a cast iron crepe pan over medium heat; spray surface with cooking spray. Pour a thin and even layer of batter onto the heated pan; fry for 30 to 60 seconds on each side. Repeat with remaining batter, spraying the pan between each batch.