Lightly rinse an 8-inch square pan or similar shallow dish with water; do not dry it. Set it near the stove.
Pour 1 3/4 cups water (420 ml) into a small saucepan. Whisk in the agar powder while the water is cold, then bring the mixture to a full boil over medium-high heat, whisking often.
Once boiling, reduce the heat and simmer for 1 minute, whisking until the agar is completely dissolved. Pour the mixture into the prepared pan. Let it cool at room temperature for about 15 minutes, then refrigerate until firm, about 45 minutes.
Meanwhile, make the kuromitsu-style syrup. Combine the brown sugar, remaining 1/4 cup water (60 ml), and salt in a small saucepan. Bring to a gentle simmer over medium heat and stir until the sugar dissolves, about 2 to 3 minutes. Transfer to a heat-safe bowl and cool to room temperature.
Cut the chilled agar jelly into small cubes. Divide the cubes among four dessert bowls.
Add a spoonful of red bean paste and portions of the mandarin oranges, pineapple, and strawberries to each bowl. Garnish with a cherry if using.
Drizzle each bowl with the cooled black sugar syrup and serve immediately. Let everyone add extra syrup to taste.