Combine 1/2 gallon milk, sugar, and rice in a large saucepan over medium-low heat. Simmer, covered, for 1 hour, stirring frequently. Remove the pan from heat and let sit for 10 minutes.

Whisk together eggs, 1/4 cup milk, vanilla, and salt in a large bowl until well combined.

Stir the mixture into the rice, return the saucepan to low heat, and cook while stirring constantly for 2 minutes.

Pour the pudding into a 9x13-inch dish and cover with plastic wrap, folding back the corners to allow steam to escape. Allow pudding to cool to room temperature.

Remove the plastic wrap, sprinkle cinnamon over the pudding, and cover tightly with new plastic wrap. Refrigerate for 8 hours to overnight before serving.