Add the 4 eggs and 1 cup cottage cheese to a large mixing bowl, then whisk very thoroughly until the mixture is airy and mostly smooth.

Sift the 3/4 cup all-purpose flour, 2 teaspoons baking powder, 2 tablespoons granulated sugar, and 1/4 teaspoon salt directly into the egg mixture.

Add 1 teaspoon vanilla extract, then fold the batter gently just until no dry streaks remain.

Let the pancake batter rest for 10 minutes so it thickens and the flour hydrates.

Heat a nonstick skillet over medium-low heat and melt a small portion of the 1 tablespoon butter to lightly coat the cooking surface.

Spoon about 1/4 cup batter per pancake into the skillet, then cook until bubbles form and the edges look set, about 2 to 3 minutes.

Flip each pancake with a spatula, then cook the second side until golden brown and cooked through, about 1 to 2 minutes.

Repeat with the remaining batter, adding the remaining butter to the skillet as needed between batches.