Preheat the oven to 350 degrees F.
Heat a 12-inch skillet over medium-high heat. Add the oil, then the sausage. Saute the meat until browned but still a little pink, about 5 minutes. Add the shallot and continue to cook until the sausage is fully cooked, another 5 minutes. Off the heat, deglaze with the calvados and scrape up any bits on the bottom of the skillet. Add the raisins, pistachios and sage. Season with salt and pepper and set aside to cool in a bowl.
Halve the apples from stem to bottom and core. Carefully hollow them out using a melon baller, reserving the apple "balls." Chop up the apple "balls" (you should have about 3/4 cup) and add to the sausage mixture. Stuff each hollowed-out apple half with some of the sausage mixture.
Pour the vinegar into the bottom of a 9-by-13-inch baking dish and add the stuffed apples skin-side down. Bake until the apples are just soft, about 25 minutes. Top each apple with a slice of cheese and continue to bake until melted, another 5 minutes. Garnish with fresh thyme leaves.
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