Step 1
Sprinkle each side of 2 lb. skin-on, bone-in hen thighs (4–6), patted dry, with 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt and 1 tsp. freshly floor pepper. Prepare hen, pores and skin facet down, in a chilly medium cast-iron or ovenproof stainless-steel skillet and set over medium warmth. Cook dinner, undisturbed, rotating pan on burner for even browning, till pores and skin is deep golden brown and hen releases simply from pan, 25–half-hour. Switch hen to a big plate or baking sheet and prepare pores and skin facet up.
Step 2
Place a rack in center of oven; preheat to 375°. Pour off all however about 2 Tbsp. fats from pan right into a small heatproof bowl and put aside. Set pan over medium-high warmth, add 8 medium shallots, peeled, quartered via root ends, 1 giant lemon, sliced into ⅛”–¼”-thick rounds, seeds eliminated, and 12–14 pitted dates (about 8 oz.), torn in half, quartered if giant, and cook dinner, stirring sometimes, till softened and deeply browned in spots, about 5 minutes. Switch to plate with hen.
Step 3
Scale back warmth to medium and add 1 Tbsp. reserved fats to pan. Sprinkle in 1 Tbsp. all-purpose flour and cook dinner, stirring consistently, till a paste types and darkens barely, about 1 minute. Stirring consistently, step by step pour in 2 cups dry white wine; convey to a simmer. Cook dinner, stirring sometimes, till sauce is diminished to concerning the consistency of heavy cream, 10–12 minutes.
Step 4
Take away pan from warmth; add 3 Tbsp. unsalted butter, 2 tsp. Dijon mustard, and remaining ¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt and ½ tsp. freshly floor pepper and whisk till sauce is easy and emulsified. Return shallots, lemon slices, and dates to pan and stir to coat in sauce. Nestle hen, pores and skin facet up, into combination and add 4 sprigs thyme. Switch to oven; bake, uncovered, till hen is cooked via and an instant-read thermometer inserted into the thickest a part of thighs registers 165°, 25–half-hour.
