Preheat the broiler.
Put unwrapped tomatillos, whole jalapenos, garlic cloves with wrappers on, and peeled, quartered onions in a shallow pan, and broil until slightly blackened - about 5 minutes.
Let the vegetables cool. Pull the wrappers off the garlic, cut the tops off the jalapenos (but leave the seeds and insides), and trim the ends off the onions.
Put all vegetables inside a food processor, and add a big handful of cilantro and 3/4 tsp sugar. Blend until it's pulpy. It will be runny.
Heat a little olive oil in a saute pan and add the vegetable mixture. Heat, stirring, until it thickens up a bit.
Add 3/4 cup chicken broth and 1/4 cup lime juice and continue heating, stirring from time to time, until it thickens up again.