Beat eggs and sugar together in a bowl using an electric mixer on medium speed until well blended.
Mix flour and baking powder together in a separate bowl. Slowly mix into the sugar-egg mixture; batter will thicken rather quickly. Slowly add milk. Stir in vanilla extract.
Heat a lightly oiled griddle over medium-high heat. Drop batter by large spoonfuls onto the griddle and cook until bubbles form and the edges are dry, 3 to 4 minutes. Flip and cook until browned on the other side, 2 to 3 minutes. Repeat with remaining batter.
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