Whisk self-rising flour, sugar, eggs, evaporated milk, and water together in a saucepan placed over medium-high heat. Whisk constantly while bringing mixture to a boil. Reduce heat to medium-low. Whisking constantly, cook pudding at a simmer until thickened, about 15 to 20 minutes.

When pudding has thickened, stir in margarine and vanilla extract until thoroughly combined.

Remove pudding from heat and set aside for about 10 minutes to cool. Sprinkle pudding with cinnamon; serve warm.