Make the Bordelaise Garnish: Melt the butter in a large skillet over medium-high heat. Add the shallots and cook until translucent, about 5 minutes. Add the mushrooms and thyme and cook 5 minutes longer. Add the wine and cook until the liquid is reduced by half. Discard the thyme.
Make the Seared Cod: Heat the olive oil in a nonstick skillet over medium-high heat. Season the fillets with salt and pepper and slip them into the pan, skin side down, along with the garlic and thyme. Sear the fillets for 3 minutes, turn them over and cook for 3 minutes more. Reduce the heat to medium, add the butter and cook another 3 minutes, or until the fish is opaque, moist and lightly firm when pressed.
Spoon the Bordelaise Garnish onto a serving platter, top with the seared cod, and sprinkle with parsley.