Position a rack in the center of the oven and heat the oven to 325°F. Season the salmon all over with salt and pepper. Let sit at room temperature while you prepare the sauce.
Melt the butter in a 12-inch ovenproof skillet over medium-high heat. Add the mushrooms and celery and cook, stirring occasionally, until the mushrooms are browned on at least one side, 3 to 5 minutes. Add the carrots and leeks and cook, stirring occasionally, until just softened, about 4 minutes (reduce the heat to medium if the pan starts to get dark). Add the tomato paste and cook, stirring, for 1 minute. Add the Pinot Noir, bay leaf, and thyme sprig, scrape the bottom of the pan with a wooden spoon to release any browned bits, and boil until the wine is reduced by about half, 2 to 4 minutes. Add the chicken broth and cream and bring to a brisk simmer.
Nestle the salmon fillets into the vegetables and pile some of the vegetables on top of the fillets to keep the fish moist. Tightly cover the pan with a lid or aluminum foil and braise in the oven until the fish is almost cooked through, 10 to 15 minutes, depending on thickness.
With a slotted spatula, transfer the salmon to 4 shallow serving bowls. Concentrate the sauce by placing the pan over medium-high heat and boiling until it’s thickened to your liking. Discard the bay leaf and thyme sprig. Stir in the chopped thyme and parsley, season to taste with salt and pepper, spoon the sauce over the salmon, and serve.
Mashed potatoes or rice pilaf makes a nice accompaniment to this dish.