Preheat the oven to 400 degrees. Pierce the potatoes with a fork; microwave for 15 minutes. Remove and brush with olive oil; transfer to the oven rack and bake until fully tender, about 15 minutes.
Meanwhile, heat 2 tablespoons oil in a medium skillet over medium heat. Stir in the flour with a wooden spoon and cook until slightly toasted, about 2 minutes. Whisk in the milk and bring to a boil. Reduce the heat and simmer, whisking occasionally, until the sauce begins to thicken, about 6 minutes. Stir in the spinach and ham and cook until the greens wilt and the mixture is about as thick as sour cream, 3 to 4 more minutes. Season with the cayenne and nutmeg and add salt to taste.
Slice the cooked potatoes lengthwise down the middle (but not all the way through); press in on the ends to open the slit. Drizzle 1/2 tablespoon oil into each potato; fluff the flesh with a fork and season with salt. Divide the spinach mixture among the potatoes and top with the shredded cheese while still hot.