In a large, heavy skillet, heat the oil over medium-high heat. Season both sides of the pork lightly with the salt and pepper. Add the medallions to the pan and cook for 2 1/2 minutes on the first side and 2 minutes on the second side. Transfer to a large plate and cover to keep warm.

Add 1 tablespoon of butter to the skillet, and when foamy, add the shallots and garlic. Cook, stirring, until soft, 1 minute. Add the white wine and simmer until reduced to 3 tablespoons, about 4 minutes. Add the cream, bring to a boil, and cook until reduced by half, about 4 minutes. Reduce the heat to medium and add the mustard, whisking to incorporate. Add the remaining tablespoon of butter, whisking to incorporate. Stir in the green peppercorns. Return the pork medallions and any accumulated juices to the pan and cook until the meat is just warmed through, about 30 seconds.

To serve, divide the potatoes among the 4 plates. Arrange 2 medallions on each plate and top with sauce. Garnish each serving with parsley and serve.

Preheat a fryer to 365 degrees F.

Using a mandolin, cut the potatoes into thin matchsticks. Fry separately, in batches, until golden brown and crispy, about 4 minutes. Remove from the oil and drain on paper towels. Season with salt.