Pat the chicken thighs dry and season both sides generously with salt and ground black pepper.
Lightly grease a large skillet with cooking spray and heat over medium-high; add the chicken thighs and pan-fry until both sides are crispy and golden brown, about 4–5 minutes per side depending on thickness.
Remove the chicken from the skillet and set aside. Discard excess oil from the pan, leaving any browned bits.
Add the tablespoon of olive oil to the skillet and reduce heat to medium; add the trimmed garlic heads and sauté until fragrant and lightly golden, about 1–2 minutes.
Pour in the chicken broth, then add the heavy whipping cream and thyme sprigs; stir to combine and bring the mixture to a gentle simmer.
Return the chicken to the skillet, season with additional salt to taste and the cayenne pepper if using, then reduce heat to low and simmer, turning the chicken once or twice, until cooked through (internal temperature 165°F / 74°C), about 6–8 minutes.
Squeeze the fresh lime juice over the chicken, spoon sauce over the top, and serve immediately.