Heat the oven to 425 degrees. On a sheet pan, toss the sweet potatoes, onion and garlic with the olive oil and season lightly with salt.
In a measuring cup, whisk the broth and mustard together until mostly smooth. Add to the pan, mixing everything together so nothing looks dry.
Pat the chicken really, really dry, especially the skin. Nestle the chicken skin-side up between the vegetables so it has contact with the pan. (It’s OK if it’s crowded.) Season the skin with the oregano, paprika and some salt, patting them to adhere to the skin. Drizzle the chicken with olive oil.
Cook until the chicken skin is very crispy and the vegetables fork-tender, 50 minutes to 1 hour, depending on the size of the thighs. Rotate the pan halfway if some parts of the pan look dry.
Squeeze half a lime over everything, and cut the remaining lime half into wedges for serving. Garnish with the cilantro and serve, stirring and scraping up anything on the bottom of the pan to spoon over the chicken and vegetables.
