Peel the plantains and cut cross-wise into 8, 1 ½” chunks.
Fill a large pot one-third full with vegetable oil and heat to 360°.
Add the plantain chunks into the hot oil and fry them about 3 minutes or until golden.
Meanwhile, make the batter: mix the flour, sugar and salt in a small bowl. Add the eggs. Gradually, stir in the milk to make a smooth batter. Cover with plastic wrap and set aside.
Remove the plantains with a slotted spoon and drain on paper towels.
Place the plantain chunks onto pieces of parchment paper or plastic and flatten them to ¼” thickness.
Place 1 cheese slice in the center of one plantain pattie and cover with another pattie, like making a sandwich, and press the edges of the plantain sandwich to enclose the cheese completely.
Dip the sandwich in the batter and add to the oil, in batches. Fry for 1 minute on each side or until golden brown. Remove with a slotted spoon and drain on paper towels. Serve warm.