Preheat oven to 375 degrees F (190 degrees C). Grease a 9x13-inch baking dish.
Mix together the garlic, shallots, white wine, chicken broth, red wine vinegar, mustard seed, salt, black pepper, and fresh thyme in a bowl, and set aside.
Place the chicken thighs into the prepared baking dish, and scatter the potatoes, mushrooms, and peas around the dish. Pour the liquid mixture over the chicken and vegetables, lifting the thighs slightly to allow the flavors to spread through the whole dish.
Bake in the preheated oven until the chicken is no longer pink in the center, the juices run clear, and an instant-read meat thermometer inserted into the center of a thigh reads at least 165 degrees F (75 degrees C), about 40 minutes. Allow dish to stand for 5 to 10 minutes before serving.