For the chicken: Preheat the oven to 400 degrees F. In a small bowl, combine the garlic, rosemary, lemon zest, 2 tablespoons of the olive oil a pinch of crushed red pepper and kosher salt to taste. Set aside.
Pat the chicken skin dry and season liberally with kosher salt. Heat a large saute pan with the remaining 1/4 cup olive oil over medium-high heat. Place the chicken skin-side down into the pan and reduce the heat to medium. Cook until the chicken is golden brown and crispy, 4 to 5 minutes. Flip the chicken and continue to cook until golden on the other side, 3 to 4 minutes. Remove the chicken to a sheet tray lined with a wire rack. Reserve the pan that the chicken was cooked in, including the fat. Brush the chicken with the rosemary and garlic mixture. Transfer to the oven and bake for 10 to 12 minutes or until the internal temperature reaches 165 degrees F.
Heat the pan that the chicken was cooked in over medium heat. Add the flour to the pan and stir with the fat to create a roux; cook for 2 minutes. Whisk in the chicken stock and a pinch of salt, then cook until the sauce has thickened, 5 minutes.
For the pilaf: Add the olive oil to a medium saucepan and turn on the heat to medium-high. Add the shallot, season with salt and cook until soft and translucent, 5 to 7 minutes. Add the rice and stir to toast for 2 minutes, ensuring the olive oil and shallot have fully coated the rice. Add the chicken stock and kosher salt. Bring to a boil, then cover, reduce to a simmer and cook until the rice is tender, 15 to 20 minutes. Fluff with a fork.
To serve: Plate a scoop of the rice, sliced chicken and gravy. Serve with green beans and garnish with chives if using.