Liberally salt and pepper the pork loin on all sides. On a sturdy work surface, slice the pork roast 4 times evenly, about 3/4 of the way down the roast. Wrap each ham slice around each cheese slice and place 1 into each of the 4 cuts. Tie the roast with kitchen string, or secure the roast closed with toothpicks. In a Dutch oven, heat 1 tablespoon oil over medium-high heat. Sear the pork loin quickly so that the roast gets color, but the cheese doesn't melt. Remove the roast and set aside.
Add the carrots and onions to the pan and cook until the onions are translucent and the vegetables are softened. Add the flour and stir to mix. Deglaze with the wine, and add the roast back into the pan along with the chicken stock and thyme. Season with salt and pepper. Cover and simmer on low for 1 hour 30 minutes.
Remove the roast from the pan once it's cooked and reduce the sauce for 5 minutes. Meanwhile, heat a large saute pan over high heat, add the remaining 1 tablespoon oil and then the mushrooms. Toss to coat in the oil and season with salt and pepper, to taste. Cook the mushrooms until they are golden, then add to the sauce. Whisk in the sour cream to the sauce. Slice the pork roast and serve with sauce poured on top. Garnish with parsley.