In a medium saucepan, combine the instant rice and 2 cups of milk. Bring to a simmer over medium heat and cook according to the rice package instructions (usually about 5 minutes). Once cooked, set it aside.
Make the Custard:
In a separate bowl, whisk the remaining 1 1/2 cups of milk, eggs, sugar, vanilla extract, and salt together until smooth and combined.
Combine and Cook:
Gradually add the egg mixture to the cooked rice, stirring constantly to avoid curdling. Place the saucepan back on the stove over low heat, and cook the pudding, stirring frequently, for about 5-8 minutes, until it thickens to a custard-like consistency. Be careful not to let it boil.
Serve:
Once thickened, remove from heat. Allow it to cool slightly, then serve warm or chilled. Garnish with a sprinkle of ground cinnamon if desired.