On shallow plate combine sugar and cinnamon until blended.
Peel bananas. Cut each one in half lengthwise; then again in half crosswise. In 10-inch skillet over medium-high heat, in 1 tablespoon hot butter, cook banana pieces until golden brown, adding more butter if necessary, turning once. Remove bananas to plate.
Cut Queso de Freir into ½-inch-thick slices. In same skillet over medium-high heat, in hot oil, cook cheese slices until well browned on both sides. Remove to cinnamon-sugar mixture to coat well on both sides.
To serve, place four banana pieces on serving plate; top with a cinnamon- sugar coated cheese slice. Repeat with remaining bananas and cheese. Serve with dulce de leche and strawberries.