In a large skillet, preferably a cast iron skillet, add 1 tablespoon oil and add the chopped potatoes. Sprinkle with salt and pepper. Cover and cook on medium heat. Turn occasionally.
After the potatoes have cooked for about 8 minutes, add sliced onions and cover the pan and cook for another 8 minutes.
While the potatoes cook, sprinkle chicken on all sides with salt and pepper.
In a separate large skillet, preferably a cast iron skillet, over medium-high heat, add oil and chicken thighs skin-side down and cook for 7-8 minutes or until skin is browned.
Turn chicken. Sprinkle with salt, pepper, Italian seasoning, and crushed red pepper, if desired. Add the minced garlic and stir.
Pour in the white wine and chicken broth. Then add the potatoes and onions. Cover and cook for 15 minutes.
Add the sugar snap peas and carrots. Cover and cook for 7 more minutes.
Sprinkle the Chicken Vesuvio with chopped parsley and serve hot.