Heat oil in a skillet over medium heat.
Flatten bread slices using a rolling pin. Mix bananas and cream cheese together in a bowl; add sugar and cinnamon and mix well. Whisk eggs in a separate bowl.
Spread about 2 1/2 tablespoons banana mixture onto 1 end of each flattened bread slice. Roll bread slice around filling. Dip bread rolls in the egg until coated and place in the hot skillet, working in batches if needed.
Cook French toast rolls in the hot oil until browned, 2 to 3 minutes per side. Repeat with remaining rolls.
Use a tall glass to flatten bread if you don’t have a rolling pin.
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