In medium saucepan over medium heat, add evaporated milk, 2 cups water, ¼ cup sugar and cinnamon stick. Bring milk mixture to simmer, stirring occasionally to dissolve sugar. Remove pot from heat; let seep 5 minutes. Remove and discard cinnamon stick.
Meanwhile, cut bread into ¾”-1” slices. In large casserole dish, arrange bread slices in single layer. Pour half of hot milk mixture over bread slices; let sit until bread absorbs milk, about 10 minutes. Using spatula, gently flip bread slices. Pour remaining milk over bread slices; let sit until bread is completely saturated, about 20 minutes more.
Meanwhile, in medium dish, beat eggs; set aside. In separate medium dish, using fork, stir together remaining sugar and ground cinnamon until well combined; set aside.
Heat oil in large, non-stick skillet or griddle over medium-high heat. Using spatula, gently transfer bread to egg mixture (bread will be very soft); flip to coat completely. Carefully lift bread slices out of egg mixture, letting excess egg drip back into dish. Cook bread slices in batches, flipping once, until puffed and golden brown on both sides, about 6 minutes.
Immediately transfer bread slices, one at a time, to dish with cinnamon sugar. Flip to coat. Serve warm.