Rinse the dried mushrooms in two changes of water, draining each time. Place the mushrooms in a small bowl with just enough warm water to cover and let soak until softened, about 30 minutes. Lift the mushrooms from the bowl and squeeze gently tp remove some of the moisture. Strain the soaking liquid through a fine mesh sieve. Reserve ¼ cup of the soaking liquid and set the mushrooms aside.

In a small saucepan melt 2 tablespoons of the butter over medium-low heat and cook the shallot until softened, about 5 minutes.

Add the wine, thyme and a generous ¼ teaspoon salt. Raise the heat to medium, simmer until the liquid is reduced by 3 tablespoons. Stir in the crème fraiche and all but 1 clove of garlic. Reduce to a bare simmer and cook, stirring occasionally, until the garlic is completely tender, 30 to 40 minutes.

Transfer the garlic mixture to a blender and puree until very smooth. Return the garlic cream to the saucepan. It should be thick enough to coat the back of a wooden spoon but still pour easily. Set aside and keep warm.

Preheat the oven at 375°.

In a small skillet melt the remaining butter over medium high heat. Crush the remaining clove of garlic and add it to the skillet. Add the mushrooms and sauté, stirring constantly, until golden at the edges. Stir in the reserved soaking liquid and salt lightly. Let the liquid nearly evaporate. Transfer to a small bowl, cover and keep warm.

Salt the chops on both sides. Wipe out the skillet and heat over medium-high heat. Add the oil and when hot, cook the chops until nicely browned on both sides, 2 to minutes using tongs to turn the meat. Stand the chops for 30 to 40 seconds on each side, bone side too until slightly golden. Place the skillet with the chops in the hot oven for 3 to 4 minutes.

Put chops in the center of each plates, reheat the garlic crème if necessary and spoon it around the chops. Scatter the mushrooms over and around the chops. Sprinkle with the parsley and serve.