Melt 2 tablespoons butter in a large skillet and set over medium heat. Cook pork chops in melted butter until both sides are lightly browned (don't worry about cooking through, yet). Transfer to a plate and cover with foil.
Melt 4 more tablespoons butter in the skillet. Cook mushrooms with lemon juice, onion, and garlic in the melted butter for about 10 minutes to soften.
Sprinkle mushrooms and onion with flour, salt, and tarragon. Stir, then slowly add broth and wine.
Place the pork chops back in the skillet. When the broth comes to a boil, turn heat down to low and put a lid on the skillet. Cook for about 20 minutes, until pork chops are cooked through.