Pat the chicken dry and season generously with salt, pepper, paprika, and a little lemon zest. Let it rest while you prep the potatoes and aromatics.
In a large, oven-safe skillet, heat the olive oil over medium-high heat. Add the chicken thighs skin-side down and cook until the skin is deeply golden and crisp, about 5-7 minutes. Flip and sear the other side for 2-3 minutes. Remove the chicken and set aside.
In the same pan, add the potatoes. Sauté for about 6-8 minutes, stirring occasionally, until they start to brown and soften. If the pan seems dry, add a splash of broth or water to prevent sticking.
Stir in the minced garlic and chopped rosemary, cooking for about 1 minute until fragrant. Return the chicken to the skillet, nestling it among the potatoes.
Pour in the lemon juice and remaining broth. Scatter a little more lemon zest on top. Bring to a gentle simmer, then cover the skillet and cook over low heat for 15-20 minutes, until the chicken is cooked through (internal temperature ~165°F) and the potatoes are tender.
Uncover and increase the heat to medium to let any excess liquid reduce to a glossy sauce, 2-4 minutes. Taste and adjust salt and pepper if needed. If you like extra brightness, finish with a quick squeeze of fresh lemon over the top.
Remove from heat and let rest for a couple of minutes before serving. Spoon the potatoes and chicken onto plates, drizzle with remaining pan juices, and garnish with a final pinch of rosemary if desired.