Marsala-Marinated Chicken With Roasted Vegetables

large shallots

Dijon mustard, plus more to taste

honey

Kosher salt and black pepper

dry Marsala

plus 6 tablespoons extra-virgin olive oil, and more to taste

bone-in, skin-on chicken thighs (about 2 pounds)

fresh oregano sprigs plus 2 tablespoons chopped fresh oregano leaves

large carrots (about 3/4 pound)

mixed mushrooms, such as cremini and shiitake (or fancier chanterelle, maitake, or morel mushrooms)

apple cider vinegar

salad greens