Preheat the oven to 375 degrees F.
Garlic-Herb Paste: Combine the rosemary, lemon zest, garlic, olive oil, cayenne, Dijon mustard, and salt and pepper to taste, in a small bowl. Stir to incorporate.
Rub chicken with Garlic-Herb Paste. Let marinate at room temperature for 1 hour.
Coat a large cast iron skillet lightly with olive oil and heat over medium-high heat. Oil the bottom of a second cast iron skillet, of equal or smaller size.
Put the chicken, skin side down, in first pan, and top it with the second pan, oiled-side down on top of the chicken. If you don't have a second cast iron skillet, use a regular pan and weigh it down with 2 heavy cans. Sear chicken until lightly browned, about 5 minutes. Remove top skillet, flip the chicken and transfer to the oven. Cook until chicken is cooked through, about 35 minutes. Transfer to a serving platter and serve.