To roast vegetables, preheat oven to 400 degrees F. Place tomatoes and rapini on a baking sheet and season with salt and pepper and coat with 1/4 cup of the olive oil. Roast the vegetables until tender, then remove and allow to cool.
Begin the Marsala sauce by heating 1/4 cup of the oil in a saute pan and cooking the shallots or onion gently until translucent. Deglaze the pan with the wine and add the stock and fresh thyme. Allow to reduce by 2/3.
For the stuffed chicken, preheat oven to 350 degrees F. Lay a long piece of plastic wrap over your cutting board and tuck it underneath the sides of the board. The chicken breasts should be placed on the covered cutting board, skin side down, with enough space between them so they can lay flat after you "butterfly" them. To make the butterfly cut, carefully slice open (without slicing the chicken all the way through) and spread the flesh of the chicken out so you will be able to pound it out into a single thin piece on which you will place stuffing and then roll up. Season the breasts with salt and pepper. Then put another length of plastic wrap over the seasoned chicken breasts and flatten with meat mallet to integrate the seasoning into the chicken. (Covering the chicken with the plastic will also keep the mess down when you pound with the meat mallet.) Pound chicken thin and remove plastic. Lay sliced smoked mozzarella on each breast followed by broccoli rabe and roasted tomatoes. Fold in each end and roll tightly, securing with toothpicks as needed, and placing on a baking sheet. Season with salt and pepper and brush with 2 tablespoons olive oil. Place in the oven and roast until fork tender about 45 to 50 minutes.
Place the potatoes on a baking sheet, season with salt and pepper, and coat with olive oil. Place in the oven and roast potatoes until they are also fork tender.
Strain Marsala sauce and whisk in butter to finish. Season with salt and pepper, as needed.
Remove any toothpicks securing the chicken. Slice each chicken roll to reveal the stuffed interior. Place on serving plate with roasted potatoes. Spoon Marsala sauce around chicken. Garnish with chopped chives.