In large bowl, stir the flour and sugar together. With an electric mixer, beat in eggs one at a time while adding 1/3 cup of milk with each egg. Mix until the batter is smooth and stretches like a ribbon.
Coarsely chop the bananas and place them in a bowl. with fork, mash the bananas into a smooth puree. Stir the puree into the batter and let the mixture rest for at least 30 minutes in a warm place before frying.
Pour the oil into a deep saucepan to a depth of 2 to 3 inches and heat to 365 degrees (really important) Drop 2 tablespoons banana batter into the hot oil, deep-frying 2 or 3 fritter at a time leaving enough space so they can spread.
Fry until golden brown, turning once with slotted spoon. Drain on paper towels. Sprinkle with confectioners' sugar and serve warm.