Step 1
Season 4 hen legs (thigh and drumstick; about 2½ lb. complete), patted dry, generously throughout with kosher salt. Warmth 2 Tbsp. extra-virgin olive oil in a big Dutch oven or different heavy pot over medium-high. Prepare dinner 2 hen legs, pores and skin aspect down, till golden brown and crisp beneath, about 5 minutes. Flip over and cook dinner till golden brown on the opposite aspect, 2–3 minutes. Switch hen to a big plate. Repeat with remaining 2 legs, adjusting warmth as wanted to maintain hen from scorching (pot might be a lot hotter at this level and second batch will brown quicker).
Step 2
Take away pot from warmth and pour off all however ¼ cup fats; discard. Add 1 massive onion, finely chopped, and 3 garlic cloves, thinly sliced, to pot and return to medium-high warmth. Prepare dinner, stirring often, till softened, about 4 minutes. Sprinkle in 1 Tbsp. plus 1½ tsp. smoked paprika and 1 Tbsp. floor cumin and cook dinner, stirring usually, till spices are evenly distributed and aromatic, about 1 minute. Add 1½ cups basmati or different long-grain rice, rinsed till water runs virtually clear, and 2¼ tsp. Diamond Crystal or 1½ tsp. Morton kosher salt; cook dinner, stirring usually, till rice is toasted, about 1 minute. Add 3 Tbsp. sherry vinegar or pink wine vinegar; cook dinner, stirring and scraping up browned bits caught to backside of pot usually, till liquid is absorbed, about 30 seconds.
Step 3
Stir in 1¾ cups low-sodium hen broth, improve warmth to excessive, and convey to a boil. Nestle hen legs, pores and skin aspect up, into rice. Cowl, scale back warmth to low, and cook dinner till hen is tender and rice is cooked by way of, 22–27 minutes. Take away from warmth and let sit 10 minutes (resist peeking right here). Uncover and fluff rice with a fork.
Step 4
In the meantime, toss 1½ cups inexperienced olives, pitted, coarsely chopped, ⅓ cup finely chopped parsley, 1 garlic clove, finely grated, remaining ¼ cup extra-virgin olive oil, and remaining 3 Tbsp. sherry vinegar or pink wine vinegar in a small bowl to mix; season olive gremolata with salt.
Step 5
Spoon some olive gremolata over hen in pot, then serve
hen with remaining olive gremolata alongside.
