In a large heavy skillet, heat about 2 inches (5cm) of vegetable oil over medium-high until oil is hot enough that it sizzles.
By hand, pick up each one of the milk-soaked bread slices (handling it gently) and dip it into the beaten eggs, coating both sides and allowing the excess to drip back into the egg bowl. Place the bread into the hot oil, and cook until well-browned on one side, about 1 to 1½ minutes. Flip the bread and cook until both sides are golden brown. Carefully transfer rabanadas to the sheet lined with paper towels.
Repeat with remaining slices of bread, cooking several simultaneously if the skillet is large enough.
NOTE: Cook in batches and do not overcrowd the pan! You may have to lower the heat a bit for the next batches or cook slices in less time since temperature will be higher.
In a medium bowl, mix sugar and cinnamon together. Dredge all sides of the bread slices into mixture. Any excess cooked eggs threads can be removed before dredging bread slices into the sugar cinnamon mixture.