Sprinkle chicken all over with salt at least 30 minutes and up to 1 day ahead (chill, covered, if more than 30 minutes).

Put ground saffron in a small bowl along with 2 tablespoons hot (not boiling) water and the rose water, if using. Stir to combine then let steep 5 minutes.

Heat a 12-inch frying pan over medium heat. Add oil, then arrange onion slices in a single layer; sprinkle with a little sea salt. Scatter garlic over onions. Place chicken thighs on top in one layer if possible (a little overlap is fine as they’ll shrink as they cook). Sprinkle with pepper, then lemon juice, then saffron water. If any saffron remains in bowl, add a bit of hot water, swirl and add to chicken.

Bring to a simmer, partially cover, and reduce heat to medium-low. Cook, turning a few times to coat in juices, until cooked through, 45 minutes to 1 hour.

Lift cooked chicken to a cutting board. Holding each thigh steady with tongs or your fingers, cut meat off bone into bite-sized pieces. Meanwhile add broth or wine to to pan juices and reduce in pan over high heat to about 3/4 cup. Add vanilla and stir well. Return chicken to sauce and set aside, covered, until ready to use.