Coarsely chop the peanuts in a food processor. Add 1/3 cup of the sugar, oil and 3 tablespoons water. Mix to form a paste.
Now let's make the dough.
In a saucepan, heat 1/3 cup of the sugar with the water until the sugar dissolves.
Place the flour in a large bowl and make a well in the center. Add the sugar water a little at a time, until you have a soft dough. Knead for a few minutes. Divide into 15 equal sized balls.
Fill a bowl with water.
Place the sesame seeds on a plate.
Make a cup in your hand with one of the balls of dough and put 2 teaspoons of the peanut filling into the cup. Bring up the dough around the filling to seal.
Dip the ball in the bowl of water and then roll in the sesame seeds. Repeat with the remaining balls.
Pour oil about 1" deep in a large skillet or wok. Place the balls in the hot oil and fry until golden brown on all sides. Drain on paper towels.
Serve warm or at room temperature.