Preheat oven to 400 degrees.
In a large Dutch oven or cast iron skillet, heat 1 tablespoon of olive oil over medium high heat. Season chicken breasts liberally with sea salt and pepper and, when the pan is hot, place breasts in it, skin-side-down.
Sear the chicken for 7 minutes or until the skin gets crispy and golden brown. Flip breasts and sear another 4 minutes; then turn off heat. Remove from pan, but leave the drippings.
Add the cauliflower florets, shallots and remaining 2 tablespoons of olive oil to the pan and season with sea salt and pepper. Stir vegetables to coat well in the chicken fat and olive oil. Pour in wine and arrange chicken breasts on top of the vegetables.
Roast uncovered for 45 - 50 minutes, stirring once halfway through, until chicken breasts are fully cooked and a meat thermometer inserted in the thickest part reaches an internal temperature of 165 degrees fahrenheit, and the cauliflower is tender.