Preheat oven to 350°. Pat chicken thighs dry and season generously all over with kosher salt. Sprinkle evenly on both sides with flour.

Heat the extra-virgin olive oil in a large cast-iron or high-sided skillet over medium. Cook chicken, skin side down, undisturbed, until thighs release easily from pan, 7–9 minutes. Turn chicken over and cook on other side until golden brown underneath, about 5 minutes. Transfer chicken to a plate and arrange skin side up.

Cook the red onion in same pan, stirring occasionally, until slightly softened and starting to turn golden brown, about 5 minutes. Add the garlic cloves and thyme sprigs and cook, stirring, until garlic is fragrant, 1–2 minutes. Pour in the cup apple cider vinegar, scraping up any browned bits. Add the Dijon mustard, honey, Worcestershire sauce, freshly ground pepper, and ¼ cup water and stir to combine. Remove pan from heat and mix sliced peaches into onion mixture. Return chicken to skillet, arranging skin side up.

Transfer pan to oven and bake just until peaches and chicken thighs are cooked through (an instant-read thermometer inserted into the thickest part of a thigh without touching the bone should register 165°), 17–20 minutes. Remove pan from oven and scatter a few more thyme sprigs over chicken to serve.