Mix the eggs, water, flour and 1/2 cup sugar. Strain through a metal sieve to remove any lumps that might remain. Spoon 5 tablespoons batter into an 8-inch diameter non-stick skillet over low heat. Spread the batter out to the edge of the pan, making a round pancake shape that is thin and smooth. Cook over medium heat until the batter has turned a light brown throughout; then add 1/2 tablespoon of butter on top of the pancake and let it melt. With a spatula, turn the pancake and let it cook until both sides are lightly crisp. Combine 3 tablespoons of peanut butter with reamaining 1/2 cup sugar mixture on the center of the pancake. Now cover the peanut butter filling by first folding over the left third of the pancake over the center third; then fold the right side over the fold, to form a vertical shape. Use a bit of batter to seal the edges. Next, fold the top and bottom of the pancake in the same fashion, making a roughly 5-inch by 4-inch rectangle. Using the spatula, lightly pat the folded pancake a few imes to flatten out the filling. Continue to pan-fry for 4 more minutes until both sides are crispy and light brown. To serve: Place the pancake on a plate and cut into 6 squares. Serve warm as is or with a topping of lightly whipped cream.