In a small sauce pan melt the butter over medium-low heat and cook the shallots until softened, about 5 minutes.
Add the wine, thyme and a generous ¼ teaspoon salt. Raise the heat to medium and simmer until the liquid is reduced to 2 tablespoons. Stir in the heavy cream and the buttermilk and all the garlic cloves.
Return to a bare simmer and cook, stirring occasionally, until the garlic is completely tender, 40 to 45 minutes.
Transfer the garlic mixture to a blender and puree until very smooth, about 1 minute. Return the garlic sauce to the saucepan. It should be thick enough to cover the back of a wooden spoon but easy to pour. Set aside covered to keep warm.
Preheat oven to 375°.
Salt and pepper generously the pork chops. In a large skillet over medium high heat add the oil. When hot add the chops and sear them on each side, 2 minutes each sides.
Remove from the stove and place in the hot oven. Cook for 3 minutes at 375° then lower the heat to 300° for another 5 minutes. The chops need to be springy to the touch and golden brown on the outside.