Rinse the dried adzuki beans. Place them in a large bowl and cover with plenty of water. Let soak for at least 8 hours or overnight.

Drain the soaked beans and transfer them to a large pot. Cover with 4 cups of fresh water. Bring to a boil, then reduce heat to a simmer. Cook for 60-90 minutes, until the beans are very soft and easily mashed.

For a chunky paste, drain any excess water and mash the beans directly in the pot. For a smooth paste, transfer the beans and a small amount of cooking liquid to a blender and process until smooth. For an extra-smooth texture, push the puree through a fine-mesh sieve.

Return the mashed or pureed beans to the pot over medium heat. Add the sugar and salt. Stir continuously until the sugar dissolves and the mixture thickens, about 10-15 minutes. The paste is ready when a spatula dragged across the bottom of the pot leaves a clear trail.

Remove from heat and let it cool completely. The paste will thicken further as it cools. Store in an airtight container in the refrigerator.