Place a rack in middle of oven; preheat to 350°. Sprinkle 2½-3-lb. skin-on, bone-in chicken leg quarters (about 4 large) all over with 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt; season generously with freshly ground pepper. Pour 2 Tbsp. extra-virgin olive oil into a cold large ovenproof high-sided skillet. Arrange chicken, skin side down, in pan and set over medium heat. Cook, undisturbed, rotating pan around on burner for even browning, until skin is deep golden brown and chicken releases easily from pan, 14-17 minutes. Transfer chicken to a plate and arrange skin side up.

Pour off all but 1 Tbsp. fat from pan; discard or save for another use. Return pan to medium heat; cook 6 medium leeks (about 1 lb.), white and pale green parts only, halved lengthwise, sliced on a deep diagonal into 3"-long pieces, 4 garlic cloves, coarsely chopped, and 1 Tbsp. all-purpose flour, stirring, until garlic is fragrant and flour is lightly toasted, about 30 seconds. Add 1½ cups fresh apple cider, ¼ cup Calvados (if using), and ¼ cup finely chopped tarragon, scraping up any browned bits. Increase heat to high and bring liquid to a simmer. Cook, stirring occasionally, until sauce is reduced by about two thirds, 9-12 minutes. Remove from heat; stir in one 7-8-oz. container crème fraîche, 1 Tbsp. apple cider vinegar, and 1 tsp. Dijon mustard and season generously with pepper. Taste sauce and season with salt if needed.

Arrange chicken, skin side up, over leeks and roast, uncovered, until chicken is cooked through and an instant-read thermometer inserted into the thickest part of a thigh registers at least 165°, 35-40 minutes.