Combine the whole milk, short-grain rice, and salt in a heavy medium saucepan. Bring to a gentle simmer over medium heat, stirring frequently to prevent sticking.
Reduce heat to low and simmer uncovered, stirring often, until the rice is tender and the mixture is creamy and slightly thick, 25–35 minutes. Adjust the heat as needed to maintain a gentle simmer and prevent scorching.
Stir in the granulated sugar and raisins. Continue cooking, stirring frequently, until the sugar dissolves, the raisins plump, and the pudding is thick but still spoonable, 5–10 minutes.
Remove from the heat and stir in the unsalted butter, vanilla extract, and ground cinnamon until smooth.
Let stand 5–10 minutes to settle and thicken further. Serve warm, or cool to room temperature and chill until cold if you prefer a firmer texture.