Bring water and 1/2 cup sugar to a boil in a small saucepan until sugar is dissolved, about 5 minutes; remove simple syrup from heat and allow to cool slightly while preparing remaining ingredients.
Mix flour, remaining 1 cup sugar, milk, and baking powder in a bowl until blended.
Heat a lightly oiled griddle over medium heat. Drop batter by large spoonfuls onto the griddle and cook until bubbles form and edges are dry, 3 to 5 minutes. Flip and cook until browned on both side, about 3 minutes more. Repeat with remaining batter.
Stir peanut butter and about 1/2 cup simple syrup in a bowl until smooth, adding more syrup as needed. Serve peanut butter sauce on top or as a dipping sauce.