Heat a large cast iron skillet over high heat. When pan begins to smoke, add tomatillos, onion, jalapenos, and garlic. Blister vegetables, turning frequently, until blackened in places but still firm, 5 minutes.
Transfer vegetables to a food processor along with cilantro, salt, and sugar and pulse until very finely chopped.
Transfer to a small saucepan and add chicken broth. Simmer over medium-high heat, stirring occasionally, until thickened slightly, 10 minutes.
Remove from heat, stir in lime juice, and cool to room temperature.
Salsa can be stored in an airtight container in the refrigerator for up to 2 weeks.