To make the nuoc cham, in a jar, mix the sugar, fish sauce, lime zest, and lime juice with a fork or whisk until the sugar is completely dissolved. Add the garlic and chilies and a few grinds of black pepper, and let everything hang out for around 30 minutes (you can eat the nuoc cham immediately, but the flavors won't be as good of friends yet). Taste and adjust if necessary (if it's too puckery, add more sugar). This keeps in an airtight container in the fridge for up to a week.
To make the salad, melt the butter in a large skillet over medium-low heat. Add the radishes, cut side down, and a pinch of salt, and sauté for 10 minutes, until they're tender and slightly browned. Turn off the heat.
Lay out the spicy greens on a serving platter or in a bowl.
Add 3 tablespoons nuoc chom to the skillet and stir to coat the radishes. Then add the chicken and brown rice and stir to combine. Immediately transfer it to the platter of greens, drizzling all the nuoc chom over the greens..
Toss gently just to coat the leaves. If you need more dressing, add more. Sprinkle over the cilantro leaves and stems and serve.