Step 1
Sprinkle both sides of 2 lb. skin-on, bone-in chicken thighs (4–6), patted dry, with 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt and 1 tsp. freshly ground pepper. Arrange chicken, skin side down, in a cold medium cast-iron or ovenproof stainless-steel skillet and set over medium heat. Cook, undisturbed, rotating pan on burner for even browning, until skin is deep golden brown and chicken releases easily from pan, 25–30 minutes. Transfer chicken to a large plate or baking sheet and arrange skin side up.
Step 2
Place a rack in middle of oven; preheat to 375°. Pour off all but about 2 Tbsp. fat from pan into a small heatproof bowl and set aside. Set pan over medium-high heat, add 8 medium shallots, peeled, quartered through root ends, 1 large lemon, sliced into ⅛”–¼”-thick rounds, seeds removed, and 12–14 pitted dates (about 8 oz.), torn in half, quartered if large, and cook, stirring occasionally, until softened and deeply browned in spots, about 5 minutes. Transfer to plate with chicken.
Step 3
Reduce heat to medium and add 1 Tbsp. reserved fat to pan. Sprinkle in 1 Tbsp. all-purpose flour and cook, stirring constantly, until a paste forms and darkens slightly, about 1 minute. Stirring constantly, gradually pour in 2 cups dry white wine; bring to a simmer. Cook, stirring occasionally, until sauce is reduced to about the consistency of heavy cream, 10–12 minutes.
Step 4
Remove pan from heat; 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 ground pepper and whisk until sauce is smooth and emulsified. Return shallots, lemon slices, and dates to pan and stir to coat in sauce. Nestle chicken, skin side up, into mixture and add 4 sprigs thyme. Transfer to oven; bake, uncovered, until chicken is cooked through and an instant-read thermometer inserted into the thickest part of thighs registers 165°, 25–30 minutes.