Rinse the rice under cool water for 10–15 seconds, then drain well.
Combine rice, water, 3 cups milk, and salt in a heavy saucepan. Bring to a gentle simmer over medium heat, stirring.
Lower heat to maintain a soft simmer. Cook uncovered, stirring often, until the rice is tender and liquid reduces, 18–22 minutes.
Stir in the remaining 1 cup milk and the sugar. Cook, stirring frequently to prevent sticking, until thick and creamy, 12–15 minutes.
Fold in cinnamon, vanilla, raisins, and butter. Cook 2–3 minutes until glossy and the raisins plump.
Remove from heat and rest 5 minutes. If too thick, loosen with a splash of milk.
Serve warm or chill for 2 hours for a firmer set. Dust with extra cinnamon if desired.