Preheat oven to 500°F and place a rack in the center.
Preheat a large, cast-iron skillet over medium-high to high heat.
Season chops inside and out with salt and pepper, fill with cheeses and julienned ham then secure edges with toothpicks. Dredge chops with seasoned flour.
Arrange potatoes in a single layer on a large baking sheet. Toss with a little olive oil and season with salt and pepper. Arrange haricots in a single layer on a second baking sheet and toss with shallots, 2 cloves crushed garlic. Season with salt and pepper.
Heat oil, 3 turns of the pan, in the skillet. Add chops and brown on each side and edges. Add 2 cloves crushed garlic to the pan and tuck sage leaves around chops; douse pan with wine or vermouth and cover. Reduce heat to medium and cook 15 minutes then remove chops to a platter and add butter to pan; swirl then add lemon juice. Spoon sauce and sage over chops.
While chops cook, bake the beans and potatoes. Beans will take about 15 minutes to get crispy at edges. Bake potatoes 15 minutes, toss and bake 5-10 more until very brown and crispy.
Serve chops topped with more sauce and potatoes and beans alongside.