Crush cardamom seeds until very fine using a rolling pin; place in a deep heavy pan. Add milk, rice, and 1 cup butter. Cook over medium heat, while slowly stirring, for 90 minutes. Reduce heat if necessary to prevent milk from boiling or overheating. Stir in sugar; continue cooking until thickens, about 15 minutes more.

Pour rice mixture into a serving bowl. Add 3 tablespoons butter on top; let melt. Dust with cinnamon. Serve warm or cold.