Season the chicken thighs evenly with kosher salt and black pepper on both sides.
Heat the olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken thighs skin-side down and cook for 5-7 minutes until the skin is golden brown and crispy. Flip and cook for another 3 minutes. Remove the chicken from the pan and set aside.
Reduce the heat to medium. Add the chopped onion to the same pan and sauté for 4-5 minutes until softened and translucent.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the rinsed rice, smoked paprika, and dried thyme. Cook for 2 minutes, stirring frequently to toast the rice lightly.
Pour in the chicken broth and stir to combine. Return the chicken thighs to the pan, placing them on top of the rice.
Bring the mixture to a simmer, then cover the pan with a tight-fitting lid. Reduce heat to low and cook for 20 minutes, or until the rice is tender and the chicken is cooked through (internal temperature 165°F/74°C).
While the rice and chicken cook, prepare the caramelized lemon slices. Heat a small nonstick skillet over medium heat.
Add the granulated sugar and spread it evenly. Place the lemon slices in a single layer on top of the sugar.
Cook for 3-4 minutes without stirring, until the sugar melts and the lemon slices begin to caramelize and turn golden. Flip the lemon slices carefully and cook for another 2 minutes. Remove from heat.
Once the chicken and rice are done, remove the pan from heat and let it rest, covered, for 5 minutes.
Gently fluff the rice with a fork and transfer the chicken and rice to serving plates.
Top each serving with 2-3 caramelized lemon slices and sprinkle with chopped fresh parsley.