Chef Bill Kim uses fresh minced chiles in his bigger batch of nuoc cham in Korean BBQ. This recipe calls for crushed red pepper for convenience, since it's only 1/8 teaspoon in our adaptation.
Preheat grill to medium-high (about 450°F).
Brush romaine halves evenly with oil. Place lettuce, cut sides down, on grates; grill 1 minute and 30 seconds. Turn lettuce; grill until lightly charred, about 1 minute and 30 seconds.
Place lettuce on a platter. Stir together 4 teaspoons water and next 5 ingredients (though red pepper) in a small bowl until sugar dissolves. Drizzle over lettuce. Top with cheese and cilantro.