Combine the raisins and the bourbon together in a small saucepan and bring to a simmer over medium heat. As soon as it reaches a simmer, remove from heat, cover, and set aside.
Bring 2 cups water to boil in large, heavy-bottomed pot (at least 3 quarts). Stir in the rice and salt; cover and simmer over low heat, stirring once or twice until the water is almost fully absorbed, 15 to 20 minutes.
Add the milk, half-and-half, and sugar. Increase the heat to medium-high to bring to a simmer, then reduce heat to maintain simmer without boiling. Cook uncovered, stirring frequently, until the mixture starts to thicken, about 30 minutes. Reduce heat to low and continue to cook, stirring every couple of minutes to prevent sticking and scorching, until a spoon is just able to stand up in the pudding, about 15 minutes longer.
Remove the pot from the heat and stir in the raisins (with any extra bourbon), vanilla extract, and cinnamon. Serve warm, at room temperature, or chilled. (It can be covered with plastic wrap on the surface of the pudding and then refrigerated up to 2 days.) You can stir in some extra milk if reheating it, to achieve the original creamy consistency, if you'd like.