For the Charleston Ice Cream:
Preheat the oven to 300°F. In a heavy stockpot, bring the water, salt, pepper, and bay leaf to a boil over medium-high heat. Reduce heat to medium, add the rice, stir once, and bring to a simmer. Simmer gently, uncovered, stirring occasionally, until the rice is al dente, about 15 minutes. Drain the rice.
Spread the rice onto a sheet tray. Dry the rice in the oven, mixing occasionally. After 10 minutes, spread the butter evenly over the rice. Continue stirring every few minutes. The rice should be dry in about 15 minutes, and the grains should separate.
To Assemble and Serve:
Plate Charleston Ice Cream in a bowl and garnish with baby lettuces.