Preheat oven to 450F.
Place the potatoes, cauliflower and garlic in a pot with tight-fitting lid. Season with salt and pepper, add stock and bring to boil. Cover and reduce heat to a simmer. Cook 10-12 minutes.
Meanwhile, heat a large, cast-iron skillet over medium-high heat. Pat the chicken dry with a paper towel, and season with salt, pepper and rosemary. Add EVOO to skillet, 2 turns of the pan. When oil smokes, add chicken skin-side down and cook 10 minutes or so, turning once.
Remove chicken to a plate and add wine to the pan, scraping up the drippings. Add potatoes, cauliflower and garlic to pan, and top with the browned chicken. Transfer to oven and cook 10-12 minutes more, until vegetables are very tender and the chicken is cooked through.
Serve chicken, potatoes and cauliflower with giardiniera alongside or topped with a little balsamic drizzle, if desired.