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Cut each pork tenderloin into 8 thick rounds to create 16 medallions, each piece about 1 – 1 ½” thick. Season both sides lightly with some of the salt and pepper.
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Heat 1 tablespoon of the oil in a large 12” skillet over medium-high heat. Once heated add 1 tablespoon of the butter and heat until the butter is melted. Add half of the medallions and sear until the bottoms are browned. Flip them over and sear the other sides, they do not have to be cooked through. Remove medallions to a plate, tent with foil, and repeat process with the remaining medallions, adding a little more oil and butter as needed.
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Add the remaining olive oil and butter to the skillet, let the butter melt. Add the shallots and sauté while stirring, until tender, about 2 minutes. Add the mushrooms and sauté the mushrooms, stirring occasionally, until browned, about 3 minutes. Stir in the thyme.
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Sprinkle with flour and stir to combine until some of the flour has cooked out. Add the wine and cook until most of the wine has evaporated and all the brown bits are picked up. Add the broth and stir to combine.
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Return the medallions and any accumulated juices to the skillet and stir to coat them completely in the sauce. Season with remaining salt and pepper, as desired. Bring to a light boil while uncovered. Reduce heat to medium-low, cover and cook for 10 - 15 minutes until the pork is cooked through and the sauce has thickened.
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Remove skillet from heat, add the sour cream and stir until the sour cream is completely combined in the sauce. Sprinkle with parsley just before serving.