Rub potatoes with a drizzle of oil and pierce skins with the tines of a fork. Microwave on high 12 minutes or until tender.
While the potatoes cook in the microwave, heat a small skillet over medium heat. Add 1 tablespoon of extra-virgin olive oil and saute chopped shallots 2 to 3 minutes or until bits are just tender. Set aside.
Cool potatoes for 5 minutes, split potatoes down the center, and scrape flesh into a bowl. Set skins aside on a non-stick baking sheet. Preheat broiler to high with oven rack 6-inches from the heat source.
To the cooked potato in the mixing bowl, add shallots, ham strips, grated cheese, butter, milk or half-and-half, thyme, and season with salt and pepper. Mash mixture with a potato masher or dinner fork until mixture is combined, but not entirely lump-free.
Scoop mixture in even amounts into skins and broil 2 or 3 minutes to lightly brown stuffed potatoes on top. Serve the halves of stuffed potatoes with salad, dark bread, and butter.