In a nonstick 12-inch skillet over medium-high, heat 2 tablespoons of oil until barely smoking. Add the chicken in an even layer and cook without stirring until well-browned, about 3 minutes.

Using tongs, flip the pieces and cook until the second sides are well-browned, another 1 to 2 minutes. Using the tongs, return the chicken to the bowl, leaving the fat in the pan.

To the same skillet over medium, add the beans and cook, stirring, until the oil is absorbed and the beans are fragrant, about 30 seconds. Transfer to the bowl with the chicken.

Set the skillet over medium-high then stir in the tomatoes and ½ teaspoon salt. Cover and cook, stirring occasionally, until browned, the liquid they released has evaporated and the mixture begins to sizzle, 5 to 7 minutes.

Stir in the remaining 2 tablespoons oil and the tomato paste and cook, stirring, until the mixture is beginning to brown, about 2 minutes. Stir in the garlic and the remaining 1 teaspoon smoked paprika, then cook until fragrant, about 30 seconds.

Add the sherry and cook, stirring occasionally, until most of the liquid has evaporated and the mixture begins to sizzle, 2 to 4 minutes.

Stir in the broth, bay, rosemary and saffron (if using), then bring to a boil over medium-high. Stir in the green beans and the cannellini bean-chicken mixture along with any accumulated juices. Sprinkle the rice into the skillet, then stir to combine and evenly distribute the grains, pressing down to ensure they are fully submerged.

Return to a boil, then reduce to medium and cook, uncovered, until most of the liquid is absorbed and craters appear in the rice, 16 to 18 minutes. Increase to medium-high and continue to cook, without stirring but rotating the pan every 10 seconds or so, until you hear sizzling and smell a toasty aroma, 1 to 2 minutes.

Remove the pan from the heat. Drape a clean kitchen towel across the top, then cover with a lid and let rest for 10 minutes. Use a wooden spoon or silicone spatula to scoop the paella onto individual plates, scraping along the pan to loosen the bottom crust (socarrat). Serve with lemon wedges.