Heat oven to 350°F. Add sugar and water to small saucepan set over medium-high heat. Bring water to boil, stirring until sugar dissolves. Using pastry brush dipped in water, clean off any sugar stuck to sides of pan. Continue to boil, without stirring, swirling pan over even cooking, until sugar caramelizes, turning deep amber, 10-12 minutes. Carefully pour caramel into heatproof 9”-diameter round pan. Set pan aside until caramel hardens and cools.
In medium saucepan over medium-high heat, heat milk, condensed milk, cinnamon and vanilla, stirring occasionally, until sides of milk begin to bubble, but milk does not boil. Remove pan from heat. Crack eggs into large, heat-proof bowl. Using whisk, lightly beat eggs. Whisk warm milk mixture into eggs, ¼ cup at a time, whisking vigorously to combine after each addition, until smooth and combined. Add dried bread to bowl, mixing to coat completely; let sit until bread is completely saturated, about 15 minutes.
Meanwhile, remove plastic wrapping from tray of ripe plantains. Microwave on high power until defrosted. Coarsely chop plantains; transfer to bowl with bread, stirring to combine.
Pour plantain mixture into prepared pan. Set pan in larger, deep baking pan. Add enough hot (not boiling) water to come half-way up the sides of round pan. Cover tightly with foil. Bake until bread pudding is puffed and thin knife inserted into center comes out clean, about 45 minutes.
Transfer bread pudding pan to cooling rack; cool to room temperature. To unmold, run thin knife around sides of pan. Invert onto serving plate. Cut into wedges; serve warm with vanilla ice cream, if desired.