Preheat a griddle to 300 degrees F (175 degrees C).

Stir together milk and vinegar in a small bowl or a 4-cup liquid measuring cup.

Whisk together flour, sugar, baking powder, baking soda, and salt in a second bowl.

Beat eggs in a large bowl until smooth. Add vanilla and milk mixture; whisk together. Add flour mixture to bowl with egg mixture and whisk until just combined. (Batter will be lumpy.) Let rest 3 minutes and gently stir again.

Melt some butter on the griddle, then carefully wipe with a paper towel. (You want just a bit of a sheen; don’t overgrease the griddle.) Spoon batter in 1/3-cup portions onto griddle.

Cook until bubbles form on surface of batter, about 2 1/2 minutes.

Flip pancakes and cook until browned on the other side, about 1 1/2 minutes more. Repeat with remaining batter.