Combine cilantro stems, ginger, garlic, shallots, chiles, and lime zest in a food processor or blender and add 1 Tbsp. light brown sugar, 1 tsp. ground coriander, and a big pinch of kosher salt. Purée, adding 1–2 Tbsp. water to loosen things up if needed, until a mostly smooth paste forms, about 1 minute. Set curry paste aside.