Bring a large pot of salted water to a boil. Add the haricots verts; cook until crisp-tender, 4 minutes. Drain and toss with 1 tablespoon each butter and parsley; season with salt and pepper. Cover to keep warm.
Meanwhile, season the pork with salt and pepper and rub with the thyme. Heat the vegetable oil in a large skillet over medium-high heat. Add the pork and cook until browned and just cooked through, 4 to 5 minutes per side. Transfer to a plate; tent with foil and let rest.
Wipe out the skillet; add the remaining 2 tablespoons butter. Add the shallot and cook, stirring, until softened, about 1 minute. Add the apples and cook, stirring, until lightly browned, about 3 minutes. Add the cider and prunes; cook until reduced by half, about 3 minutes. Add the heavy cream and cook until thickened, 3 to 5 minutes. Season with salt and pepper and stir in the remaining 2 tablespoons parsley. Serve the pork with the apple cream sauce and haricots verts.