Heat a very large skillet over medium high heat. Add the oil, then the mushrooms and garlic, season with salt and pepper, and sauté for 10 minutes until the liquid has evaporated and the mushrooms have turned nicely browned. Stir in the thyme for the last minute of cooking.
Taste and adjust seasonings, and turn into a bowl. Don’t cover the mushrooms or they will steam.
While the mushrooms are sautéing, make the pork chops. Place each pork chop in between two pieces of plastic wrap and use a rolling pin (or a bottle of wine) to gently pound the pork chops until they are of an even thickness between ¼ and ⅓-inch thick.
Place the flour in a shallow bowl, the milk in another shallow bowl, and the Panko bread crumbs in a third shallow bowl. Season the flour and the milk lightly with salt and pepper.
Season the pork lightly with salt and pepper, then dip each piece into the flour, shaking off any excess, then the milk, then the Panko, pressing so that the bread crumbs adhere to the pork. Place the breaded pork on a plate or wire rack.
Heat the oil in a large skillet until hot. Cook the pork for about 3 minutes on each side until golden brown and just cooked through; you may need to do this in two batches.
As the pieces of pork are cooked, place them briefly on a paper towel-lined plate to drain. Serve the pork with the sautéed mushrooms.