Pat the chicken thighs dry and season both sides generously with salt and black pepper.
Heat 2 tablespoons olive oil in a large skillet or sauté pan over high heat until it just begins to smoke.
Sear the thighs skin-side down until golden brown, a few minutes, then reduce heat to medium and remove the thighs from the pan.
Add the sliced onion to the pan and cook, stirring occasionally, until translucent and starting to turn golden; drain excess fat if needed.
Return the chicken to the pan, skin-side up, and pour in enough chicken broth to come about halfway up the sides of the thighs.
Arrange the 8 fresh dill sprigs over and around the thighs and sprinkle 1/2 teaspoon turmeric, a pinch of cayenne, and 1/4 teaspoon salt over the dish.
Bring the broth to a simmer, then cover the pan (vented) and reduce heat to medium-low; simmer for 40–45 minutes, basting with the cooking liquid every 10 minutes, until the meat is very tender.
Remove the thighs and discard the dill sprigs. Stir 2 tablespoons lemon juice into the pan sauce and season with additional salt and pepper to taste.
If a thicker sauce is desired, whisk 1 tablespoon water with 2 teaspoons cornstarch and add slowly to the simmering sauce until it reaches the desired consistency.
Serve the thighs topped with the reserved 1/2 tablespoon chopped fresh dill and spoon the sauce over; pair with a neutral starch if desired.
